Isolated singularities in the heat equation behaving like fractional Brownian motions

Mikihiro Fujii, Izumi Okada, Eiji Yanagida

Research output: Contribution to journalArticlepeer-review

Abstract

We consider solutions of the linear heat equation in RN with isolated singularities. It is assumed that the position of a singular point depends on time and is Hölder continuous with the exponent α∈(0,1). We show that any isolated singularity is removable if it is weaker than a certain order depending on α. We also show the optimality of the removability condition by showing the existence of a solution with a nonremovable singularity. These results are applied to the case where the singular point behaves like a fractional Brownian motion with the Hurst exponent H∈(0,1/2]. It turns out that H=1/N is critical.

Original languageEnglish
Article number125322
JournalJournal of Mathematical Analysis and Applications
Volume504
Issue number1
DOIs
Publication statusPublished - Dec 1 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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