Faber–Krahn inequalities in sharp quantitative form
By Lorenzo Brasco, Guido De Philippis, Bozhidar Velichkov. 2013
132 citations recorded by the source corpus.
The classical Faber-Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet-Laplacian among sets with given volume. In this paper we prove a sharp quantitative enhancement of this result, thus confirming a conjecture by Nadirashvili and Bhattacharya-Weitsman. More generally, the result applies to every optimal Poincare-Sobolev constant for the embeddings $W^{1,2}_0(\Omega)\hookrightarrow L^q(\Omega)$.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/125117d5b04a8496ef2b6c9606363f77703ac136
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
- Serena Dipierro
- Enrico Valdinoci
- E. Vecchi
- Stefano Biagi
- P. Garain
- Lorenzo Brasco
- Erik Lindgren
- Juha Kinnunen
In Computational Theory and Mathematics
- Serena Dipierro
- Enrico Valdinoci
- E. Vecchi
- Stefano Biagi
- P. Garain
- Lorenzo Brasco
- Vicentiu D. Rădulescu
- Marco Squassina
In Mathematical Physics
- Serena Dipierro
- Enrico Valdinoci
- E. Vecchi
- Stefano Biagi
- P. Garain
- Lorenzo Brasco
- Vicentiu D. Rădulescu
- Juha Kinnunen
Citations in the corpus
- On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique (2014, background): “6) with p = 2, this idea has been crucially exploited in the recent paper [4].”
- A Faber-Krahn inequality for mixed local and nonlocal operators (2021, result): “of the corresponding ball, then the domain must necessarily be a ball), an intense research activity focused on quantitative versions of the Faber-Krahn inequality: roughly speaking, if the eigenvalue is “close to the one of the ball”, can one deduce that the domain is also “close to a ball”? Classi”