Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GLOBAL W1,2p ESTIMATES FOR NONDIVERGENCE PARABOLIC OPERATORS WITH POTENTIALS SATISFYING A REVERSE HÖLDER CONDITION

  • Pan, Guixia (School of Public Health Anhui Medical University) ;
  • Tang, Lin (LMAM, School of Mathematical Sciences Peking University)
  • Received : 2014.12.11
  • Accepted : 2017.06.19
  • Published : 2017.09.01
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Abstract

In this article, we first give the $L^p$ boundedness of the operator $D^2L^{-1}$ with BMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ 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 $H{\ddot{o}}lder$ condition.

Keywords

Acknowledgement

Supported by : NNSF of China

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