Self-similar solution for Hardy operator

摘要

We describe the large-time asymptotics of solutions to the heat equation for the fractional Laplacian with added subcrit-ical or even critical Hardy-type potential. The asymptotics is governed by a self-similar solution of the equation, obtained as a normalized limit at the origin of the kernel of the corre-sponding Feynman-Kac semigroup. COPY; 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).