Spectral upper bound for the torsion function of symmetric stable processes

Abstract

We prove a spectral upper bound for the torsion function of symmetric stable processes that holds for convex domains in ${\mathbb{R}}^d$. Our bound is explicit and captures the correct order of growth in $d$, improving upon the existing results of Giorgi and Smits (2010) and Biswas and Lőrinczi (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.

15 pages, 1 figure, to appear in Proceedings of the American Mathematical Society