HÖLDER REGULARITY OF SOLUTIONS FOR CERTAIN DEGENERATE PARABOLIC INTEGRO-DIFFERENTIAL EQUATION
Keywords:
integro-differential equation, Hölder continuity, Moser iterationDOI:
https://doi.org/10.17654/0974324324021Abstract
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.
Received: May 19, 2024
Accepted: June 21, 2024
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