Dirichlet-to-Neumann maps on bounded Lipschitz domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Behrndt, J.¹  ter Elst, A. F. M.² 

[1] Graz Univ Technol, Inst Numer Math, A-8010 Graz, Austria

[2] Univ Auckland, Dept Math, Auckland 1142, New Zealand

关键词: Dirichlet-to-Neumann map;    Neumann-to-Dirichlet map;    Schrodinger operator;    Lipschitz domain;    Linear relation;   

DOI  :  10.1016/j.jde.2015.07.012

来源: Elsevier

【 摘 要 】

The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The main objective of this paper is to present a systematic study of the Dirichlet-to-Neumann map and its inverse, the Neumann-to-Dirichlet map, in the framework of linear relations in Hilbert spaces. Our treatment is inspired by abstract methods from extension theory of symmetric operators, utilizes the general theory of linear relations and makes use of some deep results on the regularity of the solutions of boundary value problems on bounded Lipschitz domains. (C) 2015 The Authors. Published by Elsevier Inc.

【 授权许可】

Free