Parabolic Harnack inequality for the heat equation with inverse-square potential

Luisa Moschini; Alberto Tesei

doi:10.1515/FORUM.2007.017

Published by De Gruyter June 14, 2007

Parabolic Harnack inequality for the heat equation with inverse-square potential

Luisa Moschini and Alberto Tesei

From the journal Forum Mathematicum

https://doi.org/10.1515/FORUM.2007.017

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Abstract

A parabolic Harnack inequality for the equation is proved; in particular, this implies a sharp two-sided estimate for the associated heat kernel. Our approach relies on the unitary equivalence between the Schrödinger operator and the weighted Laplacian when .