HÖLDER REGULARITY OF SOLUTIONS FOR CERTAIN DEGENERATE PARABOLIC INTEGRO-DIFFERENTIAL EQUATION

Zongqing Yang; Junhui Xie

Zongqing Yang School of Mathematics and Statistics, Hubei Minzu University, Enshi Hubei 445000, P.R.China
Junhui Xie School of Mathematics and Statistics, Hubei Minzu University, Enshi Hubei 445000, P.R.China

Article ID: 2444

Keywords: integro-differential equation, Hölder continuity, Moser iteration

Abstract

In this paper, we consider the nonlinear parabolic equation with an integro-differential term. By using classical inequalities and the Moser iteration technique, we establish the estimates for $u$ and $\nabla u$. Then we prove an inequality of Poincare type. As an byproduct of our proof, we derive a Campanato type growth estimate for $u$ which follows from $L^\infty$ estimates of $\nabla u$. Besides, the Hölder continuity of solution is presented by the isomorphism theorem.

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