A note on improved differentiability for the Banach-space valued Finsler ${\hat{I}}^3$-Laplacian

Abstract

We obtain improved fractional differentiability of solutions to the Banach-space valued Finsler ${\hat{I}}^3$-Laplacian defined on a $\ddot{I}ƒ$-convex, $\ddot{I}„$-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.

v3. Final version as published in Comptes Rendus 361 (2023). Contains a simplification in the proof of the V-functional inequality Lemma 7