Self-similar solution for Hardy operator

Krzysztof Bogdan; Tomasz Jakubowski; Panki Kim; Dominika Pilarczyk

Self-similar solution for Hardy operator

Analysis of PDEs 2023-04-28 v2 Functional Analysis

Authors: Krzysztof Bogdan , Tomasz Jakubowski , Panki Kim , Dominika Pilarczyk

Abstract

We describe the large-time asymptotics of solutions to the heat equation for the fractional Laplacian with added subcritical 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 corresponding Feynman-Kac semigroup.

Keywords

heat kernel asymptotics heat equation heat kernel estimates

Cite

@article{arxiv.2203.02039,
  title  = {Self-similar solution for Hardy operator},
  author = {Krzysztof Bogdan and Tomasz Jakubowski and Panki Kim and Dominika Pilarczyk},
  journal= {arXiv preprint arXiv:2203.02039},
  year   = {2023}
}