The Laplacian with Robin Boundary Conditions on Arbitrary Domains

By Wolfgang Arendt, Mahamadi Warma. 2003

116 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/038f8b98aaed9ea2331672f8a7b157b301c5f69c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities (2008, unknown): “We refer, for instance, to [2], [3], [4], [10], [12], [13], [14], [15], [17], [25], [26], [28], [29], [35], [37], [40], [52], and the literature cited therein.”
A Variational Approach to the Isoperimetric Inequality for the Robin Eigenvalue Problem (2010, unknown): “can indeed occur as was shown by Arendt and Warma in [ 2 ] by employing arguments from capacity theory.”
Dirichlet and Neumann boundary conditions: What is in between? (2003, methodology): “This paper is based on some properties of admissible measures and relative capacity introduced in [AW].”
The Dirichlet-to-Neumann operator on rough domains (2010, methodology): “3 in [6].”
On traces of Sobolev functions on the boundary of extension domains (2009, unknown): “Warma [3] to study the Robin Laplacian on ‘arbitrary’ domains.”
Domain Perturbation for Linear and Semi-Linear Boundary Value Problems (2008, background): “It is possible to admit arbitrary domains as shown in [11,56].”
Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “Particular attention has been paid to the spectral properties of realizations with local and nonlocal Robin boundary conditions in [41, 106, 179, 180, 226, 325, 361, 413, 543, 628, 629, 665].”
An alternative approach to the Faber–Krahn inequality for Robin problems (2009, background): “As it was noticed in [1], the trace operator in this space may not be well defined for sets which have a boundary containing a very large number of points with zero density with respect to Ω.”
The Robin and Wentzell-Robin Laplacians on Lipschitz Domains (2006, background): “The boundary conditions (1) have been intensively studied in [4] (for Lipschitz domains), [ 5 ], [8] and [20] (for arbitrary domains in R N ) in the space L p (Ω).”
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, methodology): “itions involving measures on the boundary for very general domains Ω were intensively discussed in terms of quadratic forms and capacity methods in the literature, and we refer, for instance, to [5], [6], [15], [80], and the references therein. 6 F. GESZTESY AND M. MITREA (ii) In the special case θ=”
A Faber-Krahn inequality for Robin problems in any space dimension (2006, background): “1 remains true for arbitrary domains in the setting of [10] (see also [3]).”