Interior $C^{1,α}$ estimates for $p-$Laplacian equations with optimal regularity

Damiao Araujo, Lei Zhang

Published 2015-07-24Version 1

It is well known that solutions of $\Delta_p u=f$ are $C^{1,\alpha}$ as long as $f$ is sufficiently smooth. In this article we determine the optimal $\alpha$, establish interior $C^{1,\alpha^-}$ estimates and generalize the results of $p-$Laplacian equation to a class of more general equations.