Back to Search
Start Over
$L^p$ continuity of eigenprojections for 2-d Dirichlet Laplacians under perturbations of the domain
- Publication Year :
- 2024
-
Abstract
- We generalise results by Lamberti and Lanza de Cristoforis (2005) concerning the continuity of projections onto eigenspaces of self-adjoint differential operators with compact inverses as the (spatial) domain of the functions is perturbed in $\mathbb{R}^2$. Our main case of interest is the Dirichlet Laplacian. We extend these results from bounds from $H_0^1$ to $H_0^1$ to bounds from $L^p$ to $L^p$, under the assumption that $(-\Delta^{-1}-z)^{-1}$ is $L^p$ bounded when $z$ lies outside of the spectrum of $-\Delta^{-1}$. We show that this assumption is met if the initial domain is a square or a rectangle.<br />Comment: 27 pages, 2 figures
- Subjects :
- Mathematics - Analysis of PDEs
47A70 (Primary), 35P10, 42B08 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2401.10066
- Document Type :
- Working Paper