Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients

Giorgio Metafune; Chiara Spina

doi:10.3934/dcds.2012.32.2285

Article Contents

2012, Volume 32, Issue 6: 2285-2299. Doi: 10.3934/dcds.2012.32.2285

This issue Previous Article Nonradial solutions for the Klein-Gordon-Maxwell equations Next Article Fredholm's alternative for a class of almost periodic linear systems

Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients

Giorgio Metafune^1, and
Chiara Spina^1,

1.
Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, C.P.193, 73100, Lecce

Received: December 31, 2010

Revised: June 30, 2011

Published: May 2012

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Abstract

We prove heat kernel bounds for the operator $(1+|x|^\alpha)\Delta$ in $\mathbb{R}^N$, through Nash inequalities and weighted Hardy inequalities.

Keywords:

Mathematics Subject Classification: 47D07, 35B50, 35J25, 35J70.

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