THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(10)60096-3

Abstract

Abstract:

In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A\nabla u)-Vu=0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation ∂_tu-div(A\nabla u)+Vu=0, where the singular potential V belonging to the Kato-Fefferman-Phong's class. Some applications are also discussed.

Key words: Three-sphere inequality, three-cylinder inequality, singular partial differential equation, Kato-Fefferman-Phongs class, Lipschitz domain

CLC Number:

35B60

ZHANG Song-Yan. THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series B, 2010, 30(3): 993-1003.

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