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arXiv · 2203.02039

Self-similar solution for Hardy operator

Krzysztof Bogdan·Tomasz Jakubowski·Panki Kim·Dominika Pilarczyk
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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.

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Krzysztof Bogdan, Tomasz Jakubowski, Panki Kim, Dominika Pilarczyk. 2022-03-03. Self-similar solution for Hardy operator. https://arxiv.org/abs/2203.02039

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