A Faber-Krahn inequality for Robin problems in any space dimension

By Daniel Daners. 2006

181 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/05acd6f15f8502433655c0c3e07d2acc86c4e7a2

How researchers see this paper

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

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Faber–Krahn Inequalities for the Robin-Laplacian: A Free Discontinuity Approach (2015, background): “4) λβ(B) ≤ λβ(Ω) where B is a ball with |B| = |Ω|, conjectured by Pólya in 1951, has been established only quite recently by Bossel in 1986 for two dimensional smooth domains [5], and by Daners for N dimensional Lipschitz regular domains [12].”
Geometrical Structure of Laplacian Eigenfunctions (2012, background): “Daners proved that among all bounded domains Ω ⊂ R of the same volume, the ball B minimizes the first Robin eigenvalue [94, 144]”
A Variational Approach to the Isoperimetric Inequality for the Robin Eigenvalue Problem (2010, unknown): “Moreover the first eigenvalue λ1(Ω) is characterized variationally as (1.2) λ1(Ω) = min u∈W1,2(Ω) u 6=0 ∫ Ω |∇u|2 dx+ β ∫ ∂Ω u2 dHN−1∫ Ω u2 dx , where the boundary term is intended in the sense of traces.”
Domain Perturbation for Linear and Semi-Linear Boundary Value Problems (2008, methodology): “Such an approach was also used in [60] for Robin boundary conditions.”
Isoperimetric Inequalities for Eigenvalues of the Laplacian (2007, background): “16, which is not short, we refer the reader to [33].”
Rearrangement inequalities and applications to isoperimetric problems for eigenvalues (2006, background): “Bounds or optimization results for other eigenvalues of the Laplacian under Neumann boundary condition ([40, 44, 48], see also [10] for inhomogeneous problems), for Robin boundary condition ([15, 19, 20]) or for the Stekloff eigenvalue problem ([16]) have also been established.”
Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications (2015, background): “As pointed out in [10,11], much more literatures concern the principal eigenvalue for elliptic operators with Dirichlet or Robin boundary conditions; see [5–8,16,17,20,21,30,38, 46,47,56] among many others; in particular, in an extensive survey paper [32], Grebenkov and Nyuyen summarized the very re”