Lieb-Thirring type estimates for Dirichlet Laplacians on spiral-shaped domains
Juan Bory-Reyes, Diana Barseghyan (Schneiderova), Baruch Schneider
TL;DR
This paper establishes Lieb-Thirring inequalities for the eigenvalues of Dirichlet Laplacians on spiral-shaped domains, extending spectral estimates to geometries with spiral asymptotics.
Contribution
It introduces Lieb-Thirring estimates for Dirichlet Laplacians on spiral-shaped regions, a novel geometric setting for spectral inequalities.
Findings
Lieb-Thirring bounds derived for spiral domains
Eigenvalue estimates below the essential spectrum threshold
Extension of spectral inequalities to non-standard geometries
Abstract
In this paper we derive Lieb-Thirring estimates for eigenvalues of Dirichlet Laplacians below the threshold of the essential spectrum on asymptotically Archimedean spiral-shaped regions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations