The Dirichlet-to-Neumann operator on rough domains

DOI10.1016/j.jde.2011.06.017zbMath1241.47036arXiv1005.0875OpenAlexW2171179278MaRDI QIDQ639484

A. F. M. ter Elst, Wolfgang Arendt

Publication date: 22 September 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.0875

zbMATH Keywords

tracesingular boundary value problemDirichlet-to-Neumann operatorrough boundaryform methodsD-Neumann boundary value problemirreducible semigroup

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) One-parameter semigroups and linear evolution equations (47D06) Markov semigroups and applications to diffusion processes (47D07) Forms (bilinear, sesquilinear, multilinear) (47A07) PDEs with measure (35R06)

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Cites Work

• A variational approach to the isoperimetric inequality for the Robin eigenvalue problem
• One-parameter semigroups of positive operators
• Dirichlet forms and analysis on Wiener space
• Dirichlet forms and symmetric Markov processes
• The Laplacian with Robin boundary conditions on arbitrary domains
• The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions
• The Laplacian on \(C(\overline\Omega)\) with generalized Wentzell boundary conditions
• Partial differential equations. 2: Qualitative studies of linear equations
• Sectorial forms and degenerate differential operators
• Robin boundary value problems on arbitrary domains
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