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.