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

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

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 .

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Veröffentlicht in:Forum mathematicum 2007-05, Vol.19 (3), p.407-427
Hauptverfasser: Moschini, Luisa, Tesei, Alberto
Format: Artikel
Sprache:eng
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Zusammenfassung: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 .
ISSN:0933-7741
1435-5337
DOI:10.1515/FORUM.2007.017