A note on improved differentiability for the Banach-space valued Finsler $\gamma$-Laplacian

Abstract

We obtain improved fractional differentiability of solutions to the Banach-space valued Finsler $\gamma$-Laplacian defined on a $\sigma$-convex, $\tau$-smooth Banach space. The operators we consider are non-linear and very degenerately elliptic. Our results are new already in the $\mathbb R$-valued setting.