Optimal regularity  for  parabolic Schrödinger operators

Fengping Yao

doi:10.3934/cpaa.2013.12.1407

Article Contents

2013, Volume 12, Issue 3: 1407-1414. Doi: 10.3934/cpaa.2013.12.1407

This issue Previous Article Multiple solutions for a class of $(p_1, \ldots, p_n)$-biharmonic systems Next Article Controllability results for a class of one dimensional degenerate/singular parabolic equations

Optimal regularity for parabolic Schrödinger operators

Fengping Yao^1,

1.
Department of Mathematics, Shanghai University, Shanghai 200444

Received: June 30, 2011

Revised: July 31, 2012

Published: April 2013

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Abstract

In this paper we study the regularity theory for the parabolic Schrödinger operator $P=\frac{\partial}{\partial t}-\triangle+V$ under optimal conditions. As a corollary we obtain $L^p$-type regularity estimates for such operator.

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Mathematics Subject Classification: 35J10; 35K10.

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