The Hadamard formula and the Rayleigh-Faber-Krahn inequality for nonlocal eigenvalue problems
arxiv(2023)
Abstract
In this paper we obtain a Hadamard type formula for simple eigenvalues and an analog to the Rayleigh-Faber-Krahn inequality for a class of nonlocal eigenvalue problems. Such class of equations include among others, the classical nonlocal problems with Dirichlet and Neumann conditions. The Hadamard formula is computed allowing domain perturbations given by embeddings of $n$-dimensional Riemannian manifolds (possibly with boundary) of finite volume while the Rayleigh-Faber-Krahn inequality is shown by rearrangement techniques.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined