Nonlinear Neumann-Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains

被引：45

作者：

Kohr, Mirela ^{[1
]}

Lanza de Cristoforis, Massimo ^{[2
]}

Wendland, Wolfgang L. ^{[3
]}

机构：

[1] Univ Babes Bolyai, Fac Math & Comp Sci, 1 M Kogalniceanu St, Cluj Napoca 400084, Romania

[2] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

[3] Univ Stuttgart, Inst Angew Anal & Numer Simulat, D-70569 Stuttgart, Germany

来源：

POTENTIAL ANALYSIS | 2013年 / 38卷 / 04期

关键词：

Stokes and Brinkman operators; Lipschitz domain; Nonlinear boundary value problem; Layer potential operators; BOUNDARY-VALUE-PROBLEMS; INHOMOGENEOUS DIRICHLET PROBLEM; INTEGRAL-EQUATIONS; LAPLACES-EQUATION; ELLIPTIC-SYSTEMS; ELEMENT METHOD; C-1; DOMAINS; OPERATORS; SOBOLEV; SPACES;

D O I：

10.1007/s11118-012-9310-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to use a layer potential analysis and the Leray-Schauder degree theory to show an existence result for a nonlinear Neumann-transmission problem corresponding to the Stokes and Brinkman operators on Euclidean Lipschitz domains with boundary data in L-p spaces, Sobolev spaces, and also in Besov spaces.

引用

页码：1123 / 1171

页数：49

共 84 条

[61] Convergence of the Neumann Series in BEM for the Neumann Problem of the Stokes System
Medkova, D.
[J]. ACTA APPLICANDAE MATHEMATICAE, 2011, 116 (03) : 281 - 304
[62] Integral representation of a solution of the Neumann problem for the Stokes system
Medkova, Dagmar
[J]. NUMERICAL ALGORITHMS, 2010, 54 (04) : 459 - 484
[63] Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains
Mikhailov, Sergey E.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 378 (01) : 324 - 342
[64] Mitrea D, 2001, MEM AM MATH SOC, V150, P1
[65] MITREA D, 2006, J INTEGRAL EQU APPL, V18, P361
[66] Boundary layer methods for Lipschitz domains in Riemannian manifolds
Mitrea, M
Taylor, M
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 163 (02) : 181 - 251
[67] Sobolev and Besov space estimates for solutions to second order PDE on Lipschitz domains in manifolds with Dini or Holder continuous metric tensors
Mitrea, M
Taylor, M
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (1-3) : 1 - 37
[68] Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem
Mitrea, M
Taylor, M
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 176 (01) : 1 - 79
[69] Mitrea M., 2012, ASTERISQUE, V344
[70] ON THE ANALYTICITY OF THE SEMIGROUP GENERATED BY THE STOKES OPERATOR WITH NEUMANN-TYPE BOUNDARY CONDITIONS ON LIPSCHITZ SUBDOMAINS OF RIEMANNIAN MANIFOLDS
Mitrea, Marius
Monniaux, Sylvie
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (06) : 3125 - 3157

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