Relevant bibliographies by topics / Lipschitz surface

Academic literature on the topic 'Lipschitz surface'

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Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Lipschitz surface"

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Birbrair, Lev, and Andrei Gabrielov. "Ambient Lipschitz Equivalence of Real Surface Singularities." International Mathematics Research Notices 2019, no. 20 (January 26, 2018): 6347–61. http://dx.doi.org/10.1093/imrn/rnx328.

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Abstract We present a series of examples of pairs of singular semialgebraic surfaces (germs of real semialgebraic sets of dimension two) in ${\mathbb R}^{3}$ and ${\mathbb R}^{4}$ which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent, but not ambient Lipschitz equivalent. For each singular semialgebraic surface $S\subset{\mathbb R}^{4}$, we construct infinitely many semialgebraic surfaces which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent to S, but pairwise ambient Lipschitz nonequivalent.
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Neumann, Walter D., Helge Møller Pedersen, and Anne Pichon. "Minimal surface singularities are Lipschitz normally embedded." Journal of the London Mathematical Society 101, no. 2 (September 12, 2019): 641–58. http://dx.doi.org/10.1112/jlms.12280.

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Birbrair, Lev, Alexandre Fernandes, and Walter D. Neumann. "Bi-Lipschitz geometry of complex surface singularities." Geometriae Dedicata 139, no. 1 (November 28, 2008): 259–67. http://dx.doi.org/10.1007/s10711-008-9333-2.

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KAPOOR, G. P., and SRIJANANI ANURAG PRASAD. "SMOOTHNESS OF COALESCENCE HIDDEN-VARIABLE FRACTAL INTERPOLATION SURFACES." International Journal of Bifurcation and Chaos 19, no. 07 (July 2009): 2321–33. http://dx.doi.org/10.1142/s0218127409024098.

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In the present paper, the smoothness of a Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS), as described by its Lipschitz exponent, is investigated. This is achieved by considering the simulation of a generally uneven surface using CHFIS. The influence of free variables and Lipschitz exponent on the smoothness of CHFIS is demonstrated by considering interpolation data generated from a sample surface.
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Neumann, Walter D., Helge Møller Pedersen, and Anne Pichon. "A characterization of Lipschitz normally embedded surface singularities." Journal of the London Mathematical Society 101, no. 2 (September 12, 2019): 612–40. http://dx.doi.org/10.1112/jlms.12279.

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Birbrair, Lev, Alexandre Fernandes, and Walter D. Neumann. "Bi-Lipschitz geometry of weighted homogeneous surface singularities." Mathematische Annalen 342, no. 1 (April 18, 2008): 139–44. http://dx.doi.org/10.1007/s00208-008-0225-4.

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Wang, Xiao Peng, Yuan Zhi Cheng, Ming Ming Zhao, Xiao Hua Ding, and Jing Bai. "Knee Bone Surface Registration Using the Lipschitz Optimization Algorithm." Advanced Materials Research 443-444 (January 2012): 537–41. http://dx.doi.org/10.4028/www.scientific.net/amr.443-444.537.

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We describe a technique for the registration of three dimensional (3D) knee bone surface points from MR image data sets. This technique is grounded on a mathematical theory – Lipschitz optimization. Based on this theory, we propose a global search algorithm that simultaneously determines the transformation and point correspondences. Compared with the other three registration approaches (ICP, EM-ICP, and genetic algorithms), the new proposed method achieved the highest registration accuracy on animal data.
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Buczolich, Zoltán. "Lipschitz images with fractal boundaries and their small surface wrapping." Proceedings of the American Mathematical Society 126, no. 12 (1998): 3589–95. http://dx.doi.org/10.1090/s0002-9939-98-04433-5.

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ELSCHNER, JOHANNES, and GUANGHUI HU. "SCATTERING OF PLANE ELASTIC WAVES BY THREE-DIMENSIONAL DIFFRACTION GRATINGS." Mathematical Models and Methods in Applied Sciences 22, no. 04 (April 2012): 1150019. http://dx.doi.org/10.1142/s0218202511500199.

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The reflection and transmission of a time-harmonic plane wave in an isotropic elastic medium by a three-dimensional diffraction grating is investigated. If the diffractive structure involves an impenetrable surface, we study the first, second, third and fourth kind boundary value problems for the Navier equation in an unbounded domain by the variational approach. A radiation condition based on the Rayleigh expansion of the quasi-periodic solutions is presented. Existence of solutions in Sobolev spaces is established if the grating profile is a two-dimensional Lipschitz surface, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. Similar solvability results are obtained for multilayered transmission gratings in the case of an incident pressure wave. Moreover, by a periodic Rellich identity, uniqueness of the solution to the first kind (Dirichlet) boundary value problem is established for all frequencies under the assumption that the impenetrable surface is given by the graph of a Lipschitz function.
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CHANG, TONGKEUN. "EXTENSION AND RESTRICTION THEOREMS IN ANISOTROPIC BESOV SPACES." Communications in Contemporary Mathematics 12, no. 02 (April 2010): 265–94. http://dx.doi.org/10.1142/s0219199710003774.

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In this paper, we study the extension and restriction theorems of the anisotropic Besov spaces in a Lipschitz hyper-surface in space-time domain. We hope that such theorems will be useful in solving a parabolic type equations in a time-varying domain.
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Dissertations / Theses on the topic "Lipschitz surface"

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Gracar, Peter. "Random interacting particle systems." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761028.

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Consider the graph induced by Z^d, equipped with uniformly elliptic random conductances on the edges. At time 0, place a Poisson point process of particles on Z^d and let them perform independent simple random walks with jump probabilities proportional to the conductances. It is well known that without conductances (i.e., all conductances equal to 1), an infection started from the origin and transmitted between particles that share a site spreads in all directions with positive speed. We show that a local mixing result holds for random conductance graphs and prove the existence of a special percolation structure called the Lipschitz surface. Using this structure, we show that in the setup of particles on a uniformly elliptic graph, an infection also spreads with positive speed in any direction. We prove the robustness of the framework by extending the result to infection with recovery, where we show positive speed and that the infection survives indefinitely with positive probability.
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Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Thim, Johan. "Simple Layer Potentials on Lipschitz Surfaces: An Asymptotic Approach." Doctoral thesis, Linköpings universitet, Tillämpad matematik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-16280.

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This work is devoted to the equation where S is the graph of a Lipschitz function φ on RN with small Lipschitz constant, and dS is the Euclidian surface measure. The integral in the left-hand side is referred to as a simple layer potential and f is a given function. The main objective is to find a solution u to this equation along with estimates for solutions near points on S. Our analysis is carried out in local Lp-spaces and local Sobolev spaces, and the estimates are given in terms of seminorms. In Paper 1, we consider the case when S is a hyperplane. This gives rise to the classical Riesz potential operator of order one, and we prove uniqueness of solutions in the largest class of functions for which the potential in (1) is defined as an absolutely convergent integral. We also prove an existence result and derive an asymptotic formula for solutions near a point on the surface. Our analysis allows us to obtain optimal results concerning the class of right-hand sides for which a solution to (1) exists. We also apply our results to weighted Lp- and Sobolev spaces, showing that for certain weights, the operator in question is an isomorphism between these spaces. In Paper 2, we present a fixed point theorem for a locally convex space , where the topology is given by a family of seminorms. We study the existence and uniqueness of fixed points for a mapping defined on a set . It is assumed that there exists a linear and positive operator K, acting on functions defined on the index set Ω, such that for every ,   Under some additional assumptions, one of which is the existence of a fixed point for the operator K + p( ; · ), we prove that there exists a fixed point of . For a class of elements satisfying Kn (p(u ; · ))(α) → 0 as n → ∞, we show that fixed points are unique. This class includes, in particular, the solution we construct in the paper. We give several applications, proving existence and uniqueness of solutions for two types of first and second order nonlinear differential equations in Banach spaces. We also consider pseudodifferential equations with nonlinear terms. In Paper 3, we treat equation (1) in the case when S is a general Lipschitz surface and 1 < p < ∞. Our results are presented in terms of Λ(r), which is the Lipschitz constant of φ on the ball centered at the origin with radius 2r. Estimates of solutions to (1) are provided, which can be used to obtain knowledge about behaviour near a point on S in terms of seminorms. We also show that solutions to (1) are unique if they are subject to certain growth conditions. Examples are given when specific assumptions are placed on Λ. The main tool used for both existence and uniqueness is the fixed point theorem from Paper 2. In Paper 4, we collect some properties and estimates of Riesz potential operators, and also for the operator that was used in Paper 1 and Paper 3 to invert the Riesz potential of order one on RN, for the case when the density function is either radial or has mean value zero on spheres. It turns out that these properties define invariant subspaces of the respective domains of the operators in question.
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Axelsson, Andreas. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." Phd thesis, 2002. http://hdl.handle.net/1885/46056.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface, in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Guillen, Nestor Daniel. "Regularization in phase transitions with Gibbs-Thomson law." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-12-2562.

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We study the regularity of weak solutions for the Stefan and Hele- Shaw problems with Gibbs-Thomson law under special conditions. The main result says that whenever the free boundary is Lipschitz in space and time it becomes (instantaneously) C[superscript 2,alpha] in space and its mean curvature is Hölder continuous. Additionally, a similar model related to the Signorini problem is introduced, in this case it is shown that for large times weak solutions converge to a stationary configuration.
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Book chapters on the topic "Lipschitz surface"

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Popescu-Pampu, Patrick. "Ultrametrics and Surface Singularities." In Introduction to Lipschitz Geometry of Singularities, 273–308. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61807-0_9.

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Birbrair, Lev, and Andrei Gabrielov. "Surface Singularities in $${\mathbb R}^4$$ : First Steps Towards Lipschitz Knot Theory." In Introduction to Lipschitz Geometry of Singularities, 157–66. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61807-0_6.

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Taylor, Michael. "Layer potentials on Lipschitz surfaces." In Mathematical Surveys and Monographs, 217–48. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/081/04.

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Snoussi, Jawad. "A Quick Trip into Local Singularities of Complex Curves and Surfaces." In Introduction to Lipschitz Geometry of Singularities, 45–71. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61807-0_2.

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Qian, Tao, and Pengtao Li. "Convolution Singular Integral Operators on Lipschitz Surfaces." In Singular Integrals and Fourier Theory on Lipschitz Boundaries, 117–48. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6500-3_4.

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Qian, Tao, and Pengtao Li. "Holomorphic Fourier Multipliers on Infinite Lipschitz Surfaces." In Singular Integrals and Fourier Theory on Lipschitz Boundaries, 149–67. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6500-3_5.

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Qian, Tao, and Pengtao Li. "Bounded Holomorphic Fourier Multipliers on Closed Lipschitz Surfaces." In Singular Integrals and Fourier Theory on Lipschitz Boundaries, 169–220. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6500-3_6.

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Qian, Tao, and Pengtao Li. "The Fractional Fourier Multipliers on Lipschitz Curves and Surfaces." In Singular Integrals and Fourier Theory on Lipschitz Boundaries, 221–74. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6500-3_7.

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Qian, Tao. "Hilbert Transforms on the Sphere and Lipschitz Surfaces." In Hypercomplex Analysis, 259–75. Basel: Birkhäuser Basel, 2008. http://dx.doi.org/10.1007/978-3-7643-9893-4_16.

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Zhang, Bo, and Guozheng Yan. "Integral Equation Methods for Scattering by Periodic Lipschitz Surfaces." In Integral Methods in Science and Engineering, 273–78. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8184-5_42.

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Conference papers on the topic "Lipschitz surface"

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Zheng Kai, Shen Tielong, and Yao Yu. "Filippov solutions on a Lipschitz continuous surface." In 2008 Chinese Control Conference (CCC). IEEE, 2008. http://dx.doi.org/10.1109/chicc.2008.4605726.

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Jiang, Yu, Kai Zheng, and Baoqing Yang. "Attitude control design of underactuated mass moment spacecraft based on nonsmooth Lipschitz surface." In 2014 33rd Chinese Control Conference (CCC). IEEE, 2014. http://dx.doi.org/10.1109/chicc.2014.6896593.

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Boissonnat, Jean-Daniel, and Steve Oudot. "Provably good sampling and meshing of Lipschitz surfaces." In the twenty-second annual symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1137856.1137906.

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Zheng, Kai, Guojiang Zhang, Jialu Du, and Xingcheng Wang. "Nonsmooth sliding mode control based on a class of linear Lipschitz switching surfaces." In 2010 3rd International Symposium on Systems and Control in Aeronautics and Astronautics (ISSCAA 2010). IEEE, 2010. http://dx.doi.org/10.1109/isscaa.2010.5632730.

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Xin, Huo, Guo Zhaosheng, and Zheng Kai. "Water drops on generic Lipschitz continuous surfaces in the sense of differential inclusion solutions." In 2015 34th Chinese Control Conference (CCC). IEEE, 2015. http://dx.doi.org/10.1109/chicc.2015.7259699.

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Krutitskii, P. A. "The Dirichlet problem for the diffusion equation in the exterior of non-closed Lipschitz surfaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756230.

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Krutitskii, P. A. "On the Dirichlet problem for the dissipative Helmholtz equation in the exterior of non-closed Lipschitz surfaces." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825508.

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Zeng, Hairong, Qiong Wu, and Nariman Sepehri. "On Control of a Two-Link Non-Fixed-Base Inverted Pendulum With Guaranteed Uniqueness." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61239.

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A nonlinear controller with guaranteed uniqueness of Filippov’s solution is presented for controlling a two-link non-fixed-base inverted pendulum. The control system is described by differential equations with discontinuous right-hand sides, which violates the requirements of the conventional solution theories to ordinary differential equations, i.e., the vector fields must be at least Lipschitz continuous. It has been shown that Lyapunov’s second method can be used for such non-smooth systems directly under the condition of existence and uniqueness of Filippov’s solution. For this non-smooth control system with three discontinuity surfaces, the uniqueness of the solution is studied using Filippov’s solution concept. The system itself is a nonlinear, non-autonomous dynamic system without an isolated equilibrium point, which violates the assumption of Lyapunov’s stability theory. To analyze the stability of the control system, a Lyapunov-like function is constructed, which satisfies all the requirements for a Lyapunov function. Such a function can serve as an upper bound of the region in which the pendulum can be stabilized. Simulation results are presented to validate the proposed approach.
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Reports on the topic "Lipschitz surface"

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Memoli, Facundo, Guillermo Sapiro, and Paul Thompson. Brain and Surface Warping via Minimizing Lipschitz Extensions (PREPRINT). Fort Belvoir, VA: Defense Technical Information Center, January 2006. http://dx.doi.org/10.21236/ada478383.

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