Global $W^{1,2}_p$ estimates for nondivergence parabolic operators with potentials satisfying a reverse H\

Guixia Pan; Lin Tang

doi:10.4134/JKMS.j140764

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2017; 54(5): 1357-1377

Online first article August 4, 2017 Printed September 1, 2017

https://doi.org/10.4134/JKMS.j140764

Global $W^{1,2}_p$ estimates for nondivergence parabolic operators with potentials satisfying a reverse H\"{o}lder condition

Guixia Pan and Lin Tang

Medical University, Peking University

Abstract

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Abstract

In this article, we first give the $L^{p}$ boundedness of the operator $D^{2}L^{-1}$ with BMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator $L$ with VMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition.

Keywords: parabolic operator, reverse H\"{o}lder condition, VMO, BMO

MSC numbers: Primary 35J10; Secondary 35B45, 42B25