Second-order regularity for degenerate p $p$ -Laplace type equations with log-concave weights

Abstract

We consider weighted $p$-Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log-concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp global second-order estimates. For unbounded domains, we prove local estimates at the boundary. The results are new even for the case $p=2$.