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Journal articles on the topic 'Lipschitz estimates'

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Published: 4 June 2021
Last updated: 28 January 2023

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1

Coburn, L. A. "Sharp Berezin Lipschitz estimates." Proceedings of the American Mathematical Society 135, no. 04 (April 1, 2007): 1163. http://dx.doi.org/10.1090/s0002-9939-06-08569-8.

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2

Osȩkowski, Adam. "Sharp Estimates for Lipschitz Class." Journal of Geometric Analysis 26, no. 2 (February 21, 2015): 1346–69. http://dx.doi.org/10.1007/s12220-015-9593-7.

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3

Varopoulos, N. Th. "Gaussian Estimates in Lipschitz Domains." Canadian Journal of Mathematics 55, no. 2 (April 1, 2003): 401–31. http://dx.doi.org/10.4153/cjm-2003-018-9.

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4

Bommier-Hato, Hélène. "Lipschitz estimates for the Berezin transform." Journal of Function Spaces and Applications 8, no. 2 (2010): 103–28. http://dx.doi.org/10.1155/2010/461315.

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We consider the generalized Fock spaceA2(μm), whereμmis the measure with weighte−|z|m,m > 0, with respect to the Lebesgue measure on Cn. Improving upon a recent result of L. Coburn and J. Xia, we show that for any bounded operatorXonA2(μm), the Berezin transform ofXsatisfies Lipschitz estimates.
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5

Armstrong, Scott N., and Zhongwei Shen. "Lipschitz Estimates in Almost-Periodic Homogenization." Communications on Pure and Applied Mathematics 69, no. 10 (October 1, 2015): 1882–923. http://dx.doi.org/10.1002/cpa.21616.

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6

Lu, Shanzhen, Yan Meng, and Qiang Wu. "LIPSCHITZ ESTIMATES FOR MULTILINEAR SINGULAR INTEGRALS, II." Acta Mathematica Scientia 24, no. 2 (April 2004): 291–300. http://dx.doi.org/10.1016/s0252-9602(17)30386-7.

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7

Ayre, P. J., M. G. Cowling, and F. A. Sukochev. "Operator Lipschitz estimates in the unitary setting." Proceedings of the American Mathematical Society 144, no. 3 (August 5, 2015): 1053–57. http://dx.doi.org/10.1090/proc/12833.

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8

Kenig, Carlos, and Christophe Prange. "Uniform Lipschitz Estimates in Bumpy Half-Spaces." Archive for Rational Mechanics and Analysis 216, no. 3 (November 28, 2014): 703–65. http://dx.doi.org/10.1007/s00205-014-0818-x.

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9

Xia, Jingbo. "Diagonalization Modulo Norm Ideals with Lipschitz Estimates." Journal of Functional Analysis 145, no. 2 (April 1997): 491–526. http://dx.doi.org/10.1006/jfan.1996.3036.

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10

Dong, Hongjie, and Doyoon Kim. "Lq-Estimates for stationary Stokes system with coefficients measurable in one direction." Bulletin of Mathematical Sciences 09, no. 01 (April 2019): 1950004. http://dx.doi.org/10.1142/s1664360719500048.

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We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori [Formula: see text]-estimates for any [Formula: see text] when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a [Formula: see text]-estimate and prove the solvability for any [Formula: see text] when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.
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11

Djordjevic, Jasmina. "Lp - estimates of solutions of backward doubly stochastic differential equations." Filomat 31, no. 8 (2017): 2365–79. http://dx.doi.org/10.2298/fil1708365d.

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This paper deals with a large class of nonhomogeneous backward doubly stochastic differential equations which have a more general form of the forward It? integrals. Terms under which the solutions of these equations are bounded in the Lp-sense, p ? 2, under both the Lipschitz and non-Lipschitz conditions, are given, i.e. Lp - stability for this general type of backward doubly stochastic differential equations is established.
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12

Cochran, James A., and Mark A. Lukas. "Differentiable positive definite kernels and Lipschitz continuity." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 2 (September 1988): 361–69. http://dx.doi.org/10.1017/s030500410006552x.

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AbstractReade[11] has shown that positive definite kernels K(x, t) which satisfy a Lipschitz condition of order α on a bounded region have eigenvalues which are asymptotically O(1/n1+α). In this paper we extend this result to positive definite kernels whose symmetric derivative Krr(x, t) = ∂2rK(x, t)/∂xτ ∂tτ is in Lipα and establish λn(K) = O(1/n2r+1+α). If ∂Krr/∂t is in Lipα, the anticipated asymptotic estimate is also derived.The proofs use a well-known result of Chang [2], recently rederived by Ha [5], and estimates based upon finite rank approximations to the kernels in question. In these latter estimates we employ the familiar piecewise linear ‘hat’ basis functions of approximation theory.
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13

Shen, Zhongwei. "Weighted estimates for elliptic systems on Lipschitz domains." Indiana University Mathematics Journal 55, no. 3 (2006): 1135–54. http://dx.doi.org/10.1512/iumj.2006.55.2558.

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14

Wu, Shuo, and Zhipei Niu. "Lipschitz estimates for the commutator of singular integral." Journal of Physics: Conference Series 1634 (September 2020): 012141. http://dx.doi.org/10.1088/1742-6596/1634/1/012141.

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15

Chang, Der-Chen, and Bao Qin Li. "Sobolev and Lipschitz estimates for weighted Bergman projections." Nagoya Mathematical Journal 147 (September 1997): 147–78. http://dx.doi.org/10.1017/s002776300000636x.

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AbstractLet Ω be a bounded, decoupled pseudo-convex domain of finite type in ℂn with smooth boundary. In this paper, we generalize results of Bonami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to the boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipschitz estimates, both of isotropic and anisotropic type, for these projections.
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16

Brown, Russell M., and Zhongwei Shen. "Estimates for the Stokes operator in Lipschitz domains." Indiana University Mathematics Journal 44, no. 4 (1995): 0. http://dx.doi.org/10.1512/iumj.1995.44.2025.

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17

Xing, Yuming, and Yong Wang. "BMO and Lipschitz Norm Estimates for Composite Operators." Potential Analysis 31, no. 4 (May 28, 2009): 335–44. http://dx.doi.org/10.1007/s11118-009-9137-5.

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18

Russell, B. Chase. "Homogenization in perforated domains and interior Lipschitz estimates." Journal of Differential Equations 263, no. 6 (September 2017): 3396–418. http://dx.doi.org/10.1016/j.jde.2017.04.028.

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19

Chipot, Michel, and Lawrence C. Evans. "Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 102, no. 3-4 (1986): 291–303. http://dx.doi.org/10.1017/s0308210500026378.

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SynopsisWe demonstrate local Lipschitz regularity for minimisers of certain functionals which are appropriately convex and quadratic near infinity. The proof employs a blow-up argument entailing a linearisation of the Euler—Lagrange equations “at infinity”. As a application, we prove that minimisers for the relaxed optimal design problem derived by Kohn and Strang [3] are locally Lipschitz.
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20

Li, Xuexin, Yong Wang, and Yuming Xing. "Norm Comparison Estimates for the Composite Operator." Journal of Function Spaces 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/943986.

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This paper obtains the Lipschitz and BMO norm estimates for the composite operator𝕄s∘Papplied to differential forms. Here,𝕄sis the Hardy-Littlewood maximal operator, andPis the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation.
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21

MITREA, DORINA, and MARIUS MITREA. "HÖLDER ESTIMATES FOR THE ELASTIC FAR-FIELD PATTERN WITH RESPECT TO THE BOUNDARY." Mathematical Models and Methods in Applied Sciences 09, no. 08 (November 1999): 1147–63. http://dx.doi.org/10.1142/s0218202599000518.

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We prove that under a small perturbation (in the Euclidean metric) of the boundary of a Lipschitz domain there corresponds a small variation (in the uniform norm) of the elastic far-field pattern. The corresponding estimate is of Hölder type. This is done under the assumptions that the Lipschitz character of the perturbation is bounded and that the frequency of the elastic waves is either sufficiently small or has a strictly positive imaginary part.
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22

Thim, Johan. "Two Weight Estimates for the Single Layer Potential on Lipschitz Surfaces with Small Lipschitz Constant." Potential Analysis 43, no. 1 (January 23, 2015): 79–95. http://dx.doi.org/10.1007/s11118-015-9464-7.

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23

Ali Özarslan, Mehmet, and Hüseyin Aktuğlu. "Quantitative Global Estimates for Generalized Double Szasz-Mirakjan Operators." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/613258.

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We introduce the generalized double Szász-Mirakjan operators in this paper. We obtain several quantitative estimates for these operators. These estimates help us to determine some function classes (including some Lipschitz-type spaces) which provide uniform convergence on the whole domain .
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24

Skripka, A. "Lipschitz estimates for functions of Dirac and Schrödinger operators." Journal of Mathematical Physics 62, no. 1 (January 1, 2021): 013506. http://dx.doi.org/10.1063/5.0017648.

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25

Wang, Zhiwei, and Lanzhe Liu. "Lipschitz Estimates for Multilinear Commutator of Pseudo-differential Operators." Annals of Functional Analysis 1, no. 2 (2010): 12–27. http://dx.doi.org/10.15352/afa/1399900584.

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26

Ćwiszewski, Aleksander, and Władysław Klinikowski. "Period estimates for autonomous evolution equations with Lipschitz nonlinearities." Journal of Differential Equations 309 (February 2022): 650–75. http://dx.doi.org/10.1016/j.jde.2021.11.042.

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27

Caspers, M., M. Junge, F. Sukochev, and D. Zanin. "BMO-estimates for non-commutative vector valued Lipschitz functions." Journal of Functional Analysis 278, no. 3 (February 2020): 108317. http://dx.doi.org/10.1016/j.jfa.2019.108317.

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28

Andersson, Fredrik, Marcus Carlsson, and Karl-Mikael Perfekt. "Operator-Lipschitz estimates for the singular value functional calculus." Proceedings of the American Mathematical Society 144, no. 5 (September 11, 2015): 1867–75. http://dx.doi.org/10.1090/proc/12843.

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29

Bogdan, Krzysztof. "Sharp Estimates for the Green Function in Lipschitz Domains." Journal of Mathematical Analysis and Applications 243, no. 2 (March 2000): 326–37. http://dx.doi.org/10.1006/jmaa.1999.6673.

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30

Hansen, P., B. Jaumard, and S. H. Lu. "On using estimates of Lipschitz constants in global optimization." Journal of Optimization Theory and Applications 75, no. 1 (October 1992): 195–200. http://dx.doi.org/10.1007/bf00939912.

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31

Zhu, Xiaolin, and Lanzhe Liu. "Weighted Lipschitz Estimates for Multilinear Commutator of Multiplier Operator." Vietnam Journal of Mathematics 41, no. 3 (July 5, 2013): 255–67. http://dx.doi.org/10.1007/s10013-013-0018-2.

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32

Zhou, Xiaosha. "Lipschitz estimates for multilinear commutator of Littlewood-Paley operator." Rendiconti del Circolo Matematico di Palermo 58, no. 2 (July 18, 2009): 297–310. http://dx.doi.org/10.1007/s12215-009-0024-0.

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33

Eleuteri, Michela, Paolo Marcellini, and Elvira Mascolo. "Lipschitz estimates for systems with ellipticity conditions at infinity." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 5 (September 5, 2015): 1575–603. http://dx.doi.org/10.1007/s10231-015-0529-4.

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34

Vitolo, Antonio. "Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues." Advances in Nonlinear Analysis 11, no. 1 (January 1, 2022): 1182–200. http://dx.doi.org/10.1515/anona-2022-0241.

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Abstract We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions, to our knowledge. If some eigenvalue is missing, such operators are nonlinear, degenerate, non-uniformly elliptic, neither convex nor concave. Here we prove an interior Lipschitz estimate under a non-standard assumption: that the solution exists in a larger, unbounded domain, and vanishes at infinity. In other words, we need a condition coming from far away. We also provide existence results showing that this condition is satisfied for a large class of solutions. On the occasion, we also extend a few qualitative properties of solutions, known for uniformly elliptic operators, to partial trace operators.
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35

HIRATA, KENTARO. "TWO-SIDED ESTIMATES FOR POSITIVE SOLUTIONS OF SUPERLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS." Bulletin of the Australian Mathematical Society 98, no. 3 (August 30, 2018): 465–73. http://dx.doi.org/10.1017/s000497271800093x.

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We give two-sided estimates for positive solutions of the superlinear elliptic problem$-\unicode[STIX]{x1D6E5}u=a(x)|u|^{p-1}u$with zero Dirichlet boundary condition in a bounded Lipschitz domain. Our result improves the well-knowna priori$L^{\infty }$-estimate and provides information about the boundary decay rate of solutions.
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36

Chen, Jingyi, and Elton P. Hsu. "Gradient Estimates for Harmonic Functions on Manifolds With Lipschitz Metrics." Canadian Journal of Mathematics 50, no. 6 (December 1, 1998): 1163–75. http://dx.doi.org/10.4153/cjm-1998-056-8.

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AbstractWe introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.
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37

Atifi, Khalid, Idriss Boutaayamou, Hamed Ould Sidi, and Jawad Salhi. "An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy." Abstract and Applied Analysis 2018 (December 9, 2018): 1–16. http://dx.doi.org/10.1155/2018/2067304.

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The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.
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38

Wu, Hui-Ling, and Jia-Cheng Lan. "Lipschitz Estimates for Fractional Multilinear Singular Integral on Variable Exponent Lebesgue Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/632384.

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We obtain the Lipschitz boundedness for a class of fractional multilinear operators with rough kernels on variable exponent Lebesgue spaces. Our results generalize the related conclusions on Lebesgue spaces with constant exponent.
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39

Chen, Dongxiang, and Suzhen Mao. "Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals." Journal of Function Spaces and Applications 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/128520.

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This paper is concerned with the pointwise estimates for the sharp function of the maximal multilinear commutatorsTΣb*and maximal iterated commutatorTΠb*, generalized bym-linear operatorTand a weighted Lipschitz functionb. The(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-r))boundedness and the(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-mr))boundedness are obtained for maximal multilinear commutatorTΣb*and maximal iterated commutatorTΠb*, respectively.
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40

Goebel, Kazimierz. "Remarks on retracting balls on spherical caps in \(c_{0}\), \(c\), \(l^{\infty }\) spaces." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 74, no. 1 (October 20, 2020): 45. http://dx.doi.org/10.17951/a.2020.74.1.45-55.

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For any infinite dimensional Banach space there exists a lipschitzian retraction of the closed unit ball B onto the unit sphere S. Lipschitz constants for such retractions are, in general, only roughly estimated. The paper is illustrative. It contains remarks, illustrations and estimates concerning optimal retractions onto spherical caps for sequence spaces with the uniform norm.
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41

Chen, Kun-Chu. "Stability estimate for a strongly coupled parabolic system." Tamkang Journal of Mathematics 43, no. 1 (March 31, 2012): 137–44. http://dx.doi.org/10.5556/j.tkjm.43.2012.897.

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42

Roos, Valentine. "Variational and viscosity operators for the evolutionary Hamilton–Jacobi equation." Communications in Contemporary Mathematics 21, no. 04 (May 31, 2019): 1850018. http://dx.doi.org/10.1142/s0219199718500189.

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We study the Cauchy problem for the first-order evolutionary Hamilton–Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax–Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable.
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43

Stachura, Eric, and Niklas Wellander. "Quantitative trace estimates for the Maxwell system in Lipschitz domains." Mathematical Methods in the Applied Sciences 44, no. 13 (May 2, 2021): 10635–52. http://dx.doi.org/10.1002/mma.7434.

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44

Attouchi, Amal, Hannes Luiro, and Mikko Parviainen. "Gradient and Lipschitz Estimates for Tug-of-War Type Games." SIAM Journal on Mathematical Analysis 53, no. 2 (January 2021): 1295–319. http://dx.doi.org/10.1137/19m1256816.

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45

McLean, William. "Hölder estimates for the cauchy integral on a Lipschitz contour." Journal of Integral Equations and Applications 1, no. 3 (September 1988): 435–52. http://dx.doi.org/10.1216/jie-1988-1-3-435.

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46

Lin, Yan, Zongguang Liu, and Na Xu. "WEIGHTED LIPSCHITZ ESTIMATES FOR COMMUTATORS ON WEIGHTED MORREY-HERZ SPACES." Taiwanese Journal of Mathematics 19, no. 1 (January 2015): 335–48. http://dx.doi.org/10.11650/tjm.19.2015.4497.

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47

Kwon, Ohin, and Jin Keun Seo. "Lipschitz stability estimates for translations and balls in inverse scattering." Inverse Problems 16, no. 2 (March 10, 2000): 293–301. http://dx.doi.org/10.1088/0266-5611/16/2/302.

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48

Tarama, Shigeo. "Energy estimates for regularly hyperbolic operators with log-Lipschitz coefficients." Applicable Analysis 86, no. 9 (September 2007): 1051–75. http://dx.doi.org/10.1080/00036810701460792.

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49

Pipher, Jill, and Gregory Verchota. "Area integral estimates for the biharmonic operator in Lipschitz domains." Transactions of the American Mathematical Society 327, no. 2 (February 1, 1991): 903–17. http://dx.doi.org/10.1090/s0002-9947-1991-1024776-7.

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50

Shen, Zhongwei. "On estimates of biharmonic functions on Lipschitz and convex domains." Journal of Geometric Analysis 16, no. 4 (December 2006): 721–34. http://dx.doi.org/10.1007/bf02922138.

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