A strong unique continuation property for the heat operator with Hardy type potential

Agnid Banerjee; Nicola Garofalo; Ramesh Manna

A strong unique continuation property for the heat operator with Hardy type potential

Analysis of PDEs 2020-07-01 v2

Authors: Agnid Banerjee , Nicola Garofalo , Ramesh Manna

Abstract

In this note we prove the strong unique continuation property at the origin for the solutions of the parabolic differential inequality $|\Delta u - u_t| \leq \frac{M}{|x|^2} |u|,$ with the critical inverse square potential. Our main result sharpens a previous one of Vessella concerned with the subcritical case.

Keywords

heat equation

Cite

@article{arxiv.2004.03932,
  title  = {A strong unique continuation property for the heat operator with Hardy type potential},
  author = {Agnid Banerjee and Nicola Garofalo and Ramesh Manna},
  journal= {arXiv preprint arXiv:2004.03932},
  year   = {2020}
}

Comments

Revised paper: Lemma 2.2 has been added

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