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

TL;DR

This paper improves the understanding of fractional differentiability for solutions to a non-linear, degenerate elliptic operator called the Banach-space valued Finsler gamma-Laplacian, extending known results even in the real-valued case.

Contribution

It provides new fractional differentiability results for solutions to the Banach-space valued Finsler gamma-Laplacian, including in the classical real-valued setting.

Findings

Enhanced fractional differentiability of solutions

Applicable to non-linear, degenerate elliptic operators

Results are novel even for real-valued cases

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.