Spectral upper bound for the torsion function of symmetric stable processes
Probability
2021-10-19 v3 Mathematical Physics
Analysis of PDEs
math.MP
Spectral Theory
Abstract
We prove a spectral upper bound for the torsion function of symmetric stable processes that holds for convex domains in . Our bound is explicit and captures the correct order of growth in , improving upon the existing results of Giorgi and Smits (2010) and Biswas and L\H{o}rinczi (2019). Along the way, we make progress towards a torsion analogue of Chen and Song's (2005) two-sided eigenvalue estimates for subordinate Brownian motion.
Cite
@article{arxiv.2001.04972,
title = {Spectral upper bound for the torsion function of symmetric stable processes},
author = {Hugo Panzo},
journal= {arXiv preprint arXiv:2001.04972},
year = {2021}
}
Comments
15 pages, 1 figure, to appear in Proceedings of the American Mathematical Society