Robin boundary value problems on arbitrary domains

By Daniel Daners. 2000

173 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2b047a91d54c19da2c6f7972e44fae3114c11221

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In Applied Mathematics

In Computational Theory and Mathematics

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.”
The Robin and Wentzell-Robin Laplacians on Lipschitz Domains (2006, background): “2]), B := e t 3∆R is bounded from L(Ω) into L∞(Ω) by ultracontractivity (see [8] or [20, Theorem 4.”
Sectorial forms and degenerate differential operators (2008, background): “Such boundary conditions on rough domains had been considered before by Daners [Dan] and [ArW].”
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].”
Faber–Krahn Inequalities for the Robin-Laplacian: A Free Discontinuity Approach (2015, background): “In fact, this corollary encodes the Faber-Krahn inequality for the first eigenvalue of the RobinLaplacian on arbitrary domains, including the non smooth setting of the class A(R ) (and so the family of Lipschitz sets) and even the case of arbitrary open sets for which the eigenvalues are defined thr”
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, background): “6], and subsequently in [22] (see also [23] which treats the case of the Laplacian).”
A Variational Approach to the Isoperimetric Inequality for the Robin Eigenvalue Problem (2010, background): “…of minimizers, Daners and Kennedy [10] have shown that the balls are the unique minimizers within the class of C2-domains, and the same result among the family of Lipschitz domains has been obtained by Bucur and Daners [5] (also for the case of the p-Laplacian operator, see moreover [7]).”
The heat equation with generalized Wentzell boundary condition (2002, background): “(see [27, Corollary 4.11.1/2]), so that the norm on the right hand side is equivalent to the H 1 (�) norm (see also [ 7, Section 2 ]) and to the H norm when a> 0i n� .”
The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions (2003, methodology): “have already been treated by form methods (see [3] and [5]), whereas for the Wentzell-Robin conditions (1) this seems to be new.”
Minimization problems for eigenvalues of the Laplacian (2003, background): “Open problem 15 (see [44]) For what values of α, the ratio λ2 λ1 achieves its maximum for the disk? Let us remark that Problem 14 is already stated in Daners, see [19] where a lower bound for ν1 is given.”
Domain Perturbation for Linear and Semi-Linear Boundary Value Problems (2008, background): “C] or [56]).”
Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications (2008, background): “It is well known that (39) has a unique eigenvalue, denoted by λprinc(â), which is real, simple, has an eigenfunction φprinc(â) ∈ L2(D) associated to it, and for any other eigenvalue λ of (39), Reλ < λprinc(â) (see [2, 4]).”
An alternative approach to the Faber–Krahn inequality for Robin problems (2009, methodology): “If Ω is an open set, not necessarily smooth, [7] used the space introduced by Maz’ja in [19, Section 4.”
Heat Kernel Estimates for Operators with Boundary Conditions (2000, background): “This is the parabolic counterpart of the elliptic Lp – theory of Robin boundary value problems on arbitrary domains as presented in [13].”
Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\ (2008, background): “6], and subsequently in [27] (see also [28] which treats the case of the Laplacian).”
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]).”