OPTIMAL SOBOLEV REGULARITY FOR LINEAR SECOND-ORDER DIVERGENCE ELLIPTIC OPERATORS OCCURRING IN REAL-WORLD PROBLEMS

被引：28

作者：

Disser, Karoline ^{[1
]}

Kaiser, Hans-Christoph ^{[1
]}

Rehberg, Joachim ^{[1
]}

机构：

[1] Weierstrass Inst, D-10117 Berlin, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2015年 / 47卷 / 03期

基金：

欧洲研究理事会;

关键词：

second-order divergence operators; elliptic regularity; mixed boundary conditions; discontinuous coefficients; BOUNDARY-VALUE-PROBLEMS; TRANSMISSION PROBLEMS; EQUATIONS; INTERFACE; UNIQUENESS; SYSTEMS; NEUMANN; SMOOTHNESS; EXISTENCE; SPACES;

D O I：

10.1137/140982969

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

On bounded domains Omega subset of R-3, we consider divergence-type operators -del center dot mu del, including mixed homogeneous Dirichlet and Neumann boundary conditions on partial derivative Omega \ Gamma and Gamma subset of partial derivative Omega, respectively, and discontinuous coefficient functions mu. We develop a general geometric framework for Omega, Gamma, and mu in which it is possible to prove that -del center dot mu del + 1 provides an isomorphism from W-Gamma(1,q) (Omega) to W-Gamma(-1,q) (Omega) for some q > 3. We indicate relevant examples from real-world applications.

引用

页码：1719 / 1746

页数：28

共 86 条

[1] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1. [J].