Dirichlet-to-Neumann maps on bounded Lipschitz domains
By Jussi Behrndt, A. T. Elst. 2014
62 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1a793d1a6c9435c8db37d9350527d789368b57d1
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Boundary Value Problems, Weyl Functions, and Differential Operators (2020, methodology): “Various papers based on boundary triplet techniques and related methods were published in the last decade; besides those papers listed before we mention as a selection here [18, 90, 91, 103, 107, 108, 251, 323, 324, 360, 429, 566, 568, 635, 647, 678] in which, e.”