Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

Hell, Tobias¹  Ostermann, Alexander¹ 

[1] Univ Innsbruck, Dept Math, A-6020 Innsbruck, Austria

关键词: Compatibility conditions;    Dirichlet and Neumann problems;    Poisson's equation;    Regularity;    Rectangular domains;    Corner singularities;   

DOI  :  10.1016/j.jmaa.2014.06.034

来源: Elsevier

【 摘 要 】

It is a well-known fact that the solution of Poisson's equation on a rectangle lacks regularity. Even for a smooth inhomogeneity, corner singularities arise in the derivatives of the solution. The very form of these singularities is of particular interest in numerical analysis; more precisely for the analysis of dimension splitting methods applied to parabolic equations. In this work, necessary and sufficient conditions on the inhomogeneity are derived which ensure a higher regularity of the solution of the Dirichlet or the Neumann problem - the so called compatibility conditions. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free