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Добірка наукової літератури з теми "Bessel potential space"

Автор: Grafiati

Опубліковано: 11 березня 2023

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Статті в журналах з теми "Bessel potential space"

Duduchava, R., and D. Kapanadze. "On the Prandtl Equation." gmj 6, no. 6 (December 1999): 525–36. http://dx.doi.org/10.1515/gmj.1999.525.

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Abstract The unique solvability of the airfoil (Prandtl) integro-differential equation on the semi-axis is proved in the Sobolev space and Bessel potential spaces under certain restrictions on 𝑝 and 𝑠.

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Duduchava, Roland, and Medea Tsaava. "Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain." Georgian Mathematical Journal 27, no. 2 (June 1, 2020): 211–31. http://dx.doi.org/10.1515/gmj-2019-2031.

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AbstractThe purpose of the present research is to investigate model mixed boundary value problems (BVPs) for the Helmholtz equation in a planar angular domain {\Omega_{\alpha}\subset\mathbb{R}^{2}} of magnitude α. These problems are considered in a non-classical setting when a solution is sought in the Bessel potential spaces {\mathbb{H}^{s}_{p}(\Omega_{\alpha})}, {s>\frac{1}{p}}, {1<p<\infty}. The investigation is carried out using the potential method by reducing the problems to an equivalent boundary integral equation (BIE) in the Sobolev–Slobodečkii space on a semi-infinite axis {\mathbb{W}^{{s-1/p}}_{p}(\mathbb{R}^{+})}, which is of Mellin convolution type. Applying the recent results on Mellin convolution equations in the Bessel potential spaces obtained by V. Didenko and R. Duduchava [Mellin convolution operators in Bessel potential spaces, J. Math. Anal. Appl. 443 2016, 2, 707–731], explicit conditions of the unique solvability of this BIE in the Sobolev–Slobodečkii {\mathbb{W}^{r}_{p}(\mathbb{R}^{+})} and Bessel potential {\mathbb{H}^{r}_{p}(\mathbb{R}^{+})} spaces for arbitrary r are found and used to write explicit conditions for the Fredholm property and unique solvability of the initial model BVPs for the Helmholtz equation in the non-classical setting. The same problem was investigated in a previous paper [R. Duduchava and M. Tsaava, Mixed boundary value problems for the Helmholtz equation in arbitrary 2D-sectors, Georgian Math. J. 20 2013, 3, 439–467], but there were made fatal errors. In the present paper, we correct these results.

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Treumann, Rudolf A., and Wolfgang Baumjohann. "Generalised partition functions: inferences on phase space distributions." Annales Geophysicae 34, no. 6 (June 2, 2016): 557–64. http://dx.doi.org/10.5194/angeo-34-557-2016.

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Abstract. It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

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Narimani, Ghassem. "Smooth pointwise multipliers of modulation spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 1 (May 1, 2012): 317–28. http://dx.doi.org/10.2478/v10309-012-0021-8.

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Abstract Let 1 < p, q < ∞ and s, r ∈ ℝ. It is proved that any function in the amalgam space W(Hrp(ℝd), ℓ∞), where p' is the conjugate exponent to p and Hrp′ (ℝd) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space Msp,q(ℝd), whenever r > |s| + d

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Bragg, L. R. "Derivative-type ascent formulas for kernels of some half-space Dirichlet problems." ANZIAM Journal 42, no. 2 (October 2000): 185–94. http://dx.doi.org/10.1017/s144618110001186x.

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AbstractDerivative-type ascent formulas are deduced for the kernels of certain half-space Dirichlet problems. These have the character of differentiation formulas for the Bessel functions but involve modifying variables after completing the differentiations. The Laplace equation and the equation of generalized axially-symmetric potential theory (GASPT) are considered in these. The methods employed also permit treating abstract versions of Dirichlet problems.

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Waphare, B. B., and S. G. Gajbhiv. "Pseudo-differential type operators and Gevrey spaces." Asian-European Journal of Mathematics 13, no. 01 (October 1, 2018): 2050027. http://dx.doi.org/10.1142/s1793557120500278.

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In this paper, the pseudo-differential type operator [Formula: see text] associated with the Bessel type operator [Formula: see text] defined by (2.3) involving the symbol [Formula: see text] whose derivatives satisfy certain growth conditions depending on some increasing sequences, is studied on certain Gevrey spaces. It is shown that the operator [Formula: see text] is a continuous linear map of one Gevrey space into another Gevrey space. A special pseudo-differential type operator called the Gevrey–Hankel type potential is defined and some of its properties are investigated. A variant of [Formula: see text] is also studied.

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HAMZA, Boutebba, Hakim LAKHAL, Slimani KAMEL, and Belhadi TAHAR. "The nontrivial solutions for nonlinear fractional Schrödinger-Poisson system involving new fractional operator." Advances in the Theory of Nonlinear Analysis and its Application 7, no. 1 (March 31, 2023): 121–32. http://dx.doi.org/10.31197/atnaa.1141136.

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In this paper, we investigate the existence of nontrivial solutions in the Bessel Potential space for nonlinearfractional Schrödinger-Poisson system involving distributional Riesz fractional derivative. By using themountain pass theorem in combination with the perturbation method, we prove the existence of solutions.

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Ševčovič, Daniel, and Cyril Izuchukwu Udeani. "Multidimensional Linear and Nonlinear Partial Integro-Differential Equation in Bessel Potential Spaces with Applications in Option Pricing." Mathematics 9, no. 13 (June 22, 2021): 1463. http://dx.doi.org/10.3390/math9131463.

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The purpose of this paper is to analyze solutions of a non-local nonlinear partial integro-differential equation (PIDE) in multidimensional spaces. Such class of PIDE often arises in financial modeling. We employ the theory of abstract semilinear parabolic equations in order to prove existence and uniqueness of solutions in the scale of Bessel potential spaces. We consider a wide class of Lévy measures satisfying suitable growth conditions near the origin and infinity. The novelty of the paper is the generalization of already known results in the one space dimension to the multidimensional case. We consider Black–Scholes models for option pricing on underlying assets following a Lévy stochastic process with jumps. As an application to option pricing in the one-dimensional space, we consider a general shift function arising from a nonlinear option pricing model taking into account a large trader stock-trading strategy. We prove existence and uniqueness of a solution to the nonlinear PIDE in which the shift function may depend on a prescribed large investor stock-trading strategy function.

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Chen, Wei, and Chao Zhang. "Regularity Properties and Lipschitz Spaces Adapted to High-Order Schrödinger Operators." Mathematics 10, no. 15 (July 26, 2022): 2600. http://dx.doi.org/10.3390/math10152600.

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Let be the high-order Schrödinger operator (−Δ)2+V2, where V is a non-negative potential satisfying the reverse Hölder inequality (RHq), with q>n/2 and n≥5. In this paper, we prove that when 0<α≤2−n/q, the adapted Lipschitz spaces Λα/4 we considered are equivalent to the Lipschitz space CLα associated to the Schrödinger operator L=−Δ+V. In order to obtain this characterization, we should make use of some of the results associated to (−Δ)2. We also prove the regularity properties of fractional powers (positive and negative) of the operator , Schrödinger Riesz transforms, Bessel potentials and multipliers of the Laplace transforms type associated to the high-order Schrödinger operators.

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Behzadan, A., and M. Holst. "On the Space of Locally Sobolev-Slobodeckij Functions." Journal of Function Spaces 2022 (July 18, 2022): 1–30. http://dx.doi.org/10.1155/2022/9094502.

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The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space. In this paper, we present a coherent rigorous study of some of the properties of locally Sobolev-Slobodeckij functions that are especially useful in the study of differential operators between sections of vector bundles on compact manifolds with rough metric. The results of this type in published literature generally can be found only for integer order Sobolev spaces W m , p or Bessel potential spaces H s . Here, we have presented the relevant results and their detailed proofs for Sobolev-Slobodeckij spaces W s , p where s does not need to be an integer. We also develop a number of results needed in the study of differential operators on manifolds that do not appear to be in the literature.

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Дисертації з теми "Bessel potential space"

GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.

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This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is divided in three parts. The first part is devoted to analyze strong maximum principles for fully nonlinear second order degenerate PDEs structured on Hörmander vector fields, having as a particular example fully nonlinear subelliptic PDEs on Carnot groups. These results are achieved by introducing a notion of subunit vector field for these nonlinear degenerate operators in the spirit of the seminal works on linear equations. As a byproduct, we then prove some new strong comparison principles for equations that can be written in Hamilton-Jacobi-Bellman form and Liouville theorems for some second order fully nonlinear degenerate PDEs. The second part of the thesis deals with time-dependent fractional Mean Field Game systems. These equations arise when the dynamics of the average player is described by a stable Lévy process to which corresponds a fractional Laplacian as diffusion operator. More precisely, we establish existence and uniqueness of solutions to such systems of PDEs with regularizing coupling among the equations for every order of the fractional Laplacian $sin(0,1)$. The existence of solutions is addressed via the vanishing viscosity method and we prove that in the subcritical regime the equations are satisfied in classical sense, while if $sleq1/2$ we find weak energy solutions. To this aim, we develop an appropriate functional setting based on parabolic Bessel potential spaces. We finally show uniqueness of solutions both under the Lasry-Lions monotonicity condition and for short time horizons. The last part focuses on the regularizing effect of evolutive Hamilton-Jacobi equations with Hamiltonian having superlinear growth in the gradient and unbounded right-hand side. In particular, the analysis is performed both for viscous Hamilton-Jacobi equations and its fractional counterpart in the subcritical regime via a duality method. The results are accomplished exploiting the regularity of solutions to Fokker-Planck-type PDEs with rough velocity fields in parabolic Sobolev and Bessel potential spaces respectively.

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Nguyen, Quoc-Hung. "THÉORIE NON LINÉAIRE DU POTENTIEL ET ÉQUATIONS QUASILINÉAIRES AVEC DONNÉES MESURES." Phd thesis, Université François Rabelais - Tours, 2014. http://tel.archives-ouvertes.fr/tel-01063365.

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Cette thése concerne l'existence et la régularité de solutions d'équations non-linéaires elliptiques, d'équations paraboliques et d'équations de Hesse avec mesures, et les critéres de l'existence de solutions grandes d'équations elliptiques et paraboliques non-linéaires. \textbf{Liste de publications} \begin{description} \item[1.] Avec M. F. Bidaut-Véron, L. Véron; {\em Quasilinear Lane-Emden equations with absorption and measure data,} Journal des Mathématiques Pures et Appliquées,~{\bf 102}, 315-337 (2014). \item[2] Avec L. Véron; {\em Quasilinear and Hessian type equations with exponential reaction and measure data,} Archive for Rational Mechanics and Analysis, {\bf 214}, 235-267 (2014). \item[3] Avec L. Véron; {\em Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption,} 17 pages, soumis, arXiv:1308.2956. \item[4] Avec M. F. Bidaut-Véron; {\em Stability properties for quasilinear parabolic equations with measure data,} 29 pages, á apparaître dans Journal of European Mathematical Society, arXiv:1409.1518. \item[5] Avec M. F. Bidaut-Véron; {\em Evolution equations of $p$-Laplace type with absorption or source terms and measure data}, 21 pages, á apparaître dans Communications in Contemporary Mathematics, arXiv:1409.1520. \item[6] {\em Potential estimates and quasilinear parabolic equations with measure data,} 118 pages, arXiv:1405.2587v1. \item[7] Avec L. Véron; {\em Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain,} 29 pages, soumis,\\ arXiv:1406.3850. \item[8] Avec M. F. Bidaut-Véron; {Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data,\em } 27 pages, soumis, arXiv:1407.2218. \end{description}\begin{description} \item[1.] Avec M. F. Bidaut-Véron, L. Véron; {\em Quasilinear Lane-Emden equations with absorption and measure data,} Journal des Mathématiques Pures et Appliquées,~{\bf 102}, 315-337 (2014). \item[2] Avec L. Véron; {\em Quasilinear and Hessian type equations with exponential reaction and measure data,} Archive for Rational Mechanics and Analysis, {\bf 214}, 235-267 (2014). \item[3] Avec L. Véron; {\em Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption,} 17 pages, soumis, arXiv:1308.2956. \item[4] Avec M. F. Bidaut-Véron; {\em Stability properties for quasilinear parabolic equations with measure data,} 29 pages, á apparaître dans Journal of European Mathematical Society, arXiv:1409.1518. \item[5] Avec M. F. Bidaut-Véron; {\em Evolution equations of $p$-Laplace type with absorption or source terms and measure data}, 21 pages, á apparaître dans Communications in Contemporary Mathematics, arXiv:1409.1520. \item[6] {\em Potential estimates and quasilinear parabolic equations with measure data,} 118 pages, arXiv:1405.2587v1. \item[7] Avec L. Véron; {\em Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain,} 29 pages, soumis,\\ arXiv:1406.3850. \item[8] Avec M. F. Bidaut-Véron; {Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data,\em } 27 pages, soumis, arXiv:1407.2218. \end{description}

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Частини книг з теми "Bessel potential space"

Gorgadze, Z. G. "On bessel potentials in linear spaces." In Lecture Notes in Mathematics, 103–10. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078466.

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Opic, Bohumír. "Continuous and Compact Embeddings of Bessel-Potential-Type Spaces." In Spectral Theory, Function Spaces and Inequalities, 157–96. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0263-5_10.

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de Castro, Luís Pinheiro, and Frank-Olme Speck. "Convolution Type Operators with Symmetry in Bessel Potential Spaces." In Recent Trends in Operator Theory and Partial Differential Equations, 21–49. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-47079-5_2.

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Maz’ya, Vladimir, and Tatyana Shaposhnikova. "Maximal Banach algebra in spaces of multipliers between Bessel potential spaces." In Problems and Methods in Mathematical Physics, 352–65. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8276-7_19.

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Karlovich, Yuri, and Ilya Spitkovsky. "(Semi)-Fredholmness of Convolution Operators on the Spaces of Bessel Potentials." In Toeplitz Operators and Related Topics, 122–52. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8543-0_9.

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Jones, B. Frank. "Characterization of Spaces of Bessel Potentials Related to the Heat Equation." In Pseudo-differential Operators, 143–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11074-0_5.

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Gatto, A. Eduardo, Ebner Pineda, and Wilfredo O. Urbina. "Riesz Potentials, Bessel Potentials, and Fractional Derivatives on Besov-Lipschitz Spaces for the Gaussian Measure." In Springer Proceedings in Mathematics & Statistics, 105–30. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4565-4_12.

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Rabinovich, Vladimir. "Fredholm Theory of Pseudodifferential Operators Acting in Variable Exponent Spaces of Bessel Potentials on Smooth Manifolds." In Trends in Mathematics, 615–21. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_67.

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"Chapter 6. Introduction to Besov and Bessel Potential Spaces." In Pseudodifferential and Singular Integral Operators. Berlin, Boston: DE GRUYTER, 2011. http://dx.doi.org/10.1515/9783110250312.149.

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Тези доповідей конференцій з теми "Bessel potential space"

Henninger, Stefan, Peter Jeschke, Graham Ashcroft, and Edmund Kügeler. "Time-Domain Implementation of Higher-Order Non-Reflecting Boundary Conditions for Turbomachinery Applications." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42362.

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The present paper demonstrates the time-domain implementation of arbitrary-order non-reflecting boundary conditions for a 3d non-linear time-accurate RANS solver for turbomachinery applications. The conditions are based on the 2d circumferential mode decomposition of the linearized Euler equations. The exact linearized conditions are non-local since they involve space-time Fourier/Laplace transforms. Time-local conditions of arbitrary order are obtained by approximation of the inverse Laplace transform Bessel function convolution kernel by sums of exponential functions. Likewise, this corresponds to a rational function approximation of the exact non-reflecting boundary kernel in the frequency-domain. The boundary conditions are validated against two numerical test cases. The first test case mimics Tyler-Sofrin modes present in turbomachinery applications by prescribing 2d acoustic modes in a uniform flow. The second test case is concerned with the potential contamination of blade flutter analyses by spurious reflections on artificial boundaries. For the benchmark problem Standard Configuration 10, blade flutter with non-zero inter-blade phase angle, acoustic resonance generates spinning waves susceptible to reflection. Contrasting the results of non-reflecting boundary conditions of varying order of accuracy shows that low order conditions can fail for challenging cases, which emphasizes the need for an accurate non-reflecting boundary treatment.

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Karshygina, Gulden Zh. "Optimal embeddings of Bessel and Riesz type potentials on the basis of weighted Lorentz spaces." In INTERNATIONAL CONFERENCE “FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS” (FAIA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5000613.

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Baliga, Ravi, Tom Neal Watts, and Harish Kamath. "Application of an Integrated Head Assembly Concept at Pressurized Water Reactor Commercial Nuclear Plants." In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icone22-30916.

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In a typical pressurized water reactor commercial nuclear plant, a number of components such as CRDMs, a lift rig to lift the Reactor Vessel Closure Head (RVCH), seismic restraints, missile shield, and a cooling system with large air ducts are installed on or directly over the RVCH. These components and systems are typically designed and installed individually to perform designated functions during plant operation. During refueling outages the removal of the RVCH from the pressure vessel and its subsequent re-installation on the pressure vessel for fuel loading requires individual dismantling and reassembly of these components resulting in an expensive and time-consuming process. Prior to detensioning the RVCH from the vessel, a lengthy series of steps or detailed procedures must be followed to safely remove the head area components and to store them in their designated spaces inside containment. The procedure generally includes: removal and storage of the concrete missile shield; removal and storage of CRDM cooling ducts; removal of seismic restraints; removal of head area cables; installation of the tripod assembly over the service structure; disconnecting the vent and level indicator lines; and installation of temporary lead blankets around the RVCH. Once the refueling is complete, these procedural steps are repeated in reverse order. Each procedure in the refueling process contributes significantly to the total cost associated with personnel time required to perform the refueling, power plant down time and consequent loss of electricity production, radiation exposure to personnel, and risks and costs associated with potential human errors. In addition, these components require a large amount of storage space inside containment raising the risk of having inadvertent contamination of work and storage areas. To reduce the outage duration and the associated radiation exposure to the workers, the authors have designed an Integrated Head Assembly (IHA) for Callaway nuclear plant based on Mr. Baliga’s patented design as disclosed in U.S. Patents. The IHA is an assembly of all head area components integrally attached to the RVCH so that all these components can be lifted with the RVCH in one assembly (see Figure 1). The IHA also provides a forced air convection system that improves the efficiency of the CRDM cooling. The IHA reduces a significant amount of critical path time and radiation dosage during refueling outages. Mr. Baliga’s invention has been implemented at several commercial nuclear plants in the USA (Turkey Point Units 3 and 4; Salem Units 1 and 2; DC Cook Units 1 and 2; Diablo Canyon Units 1 and 2; Davis Besse Unit 1; and Callaway Unit 1). This paper provides details of the IHA design implemented at Callaway nuclear plant in the USA.

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