Interior regularity of space derivatives to an evolutionary, symmetric $\varphi$-Laplacian

TL;DR

This paper establishes new second-order spatial regularity estimates for solutions to evolutionary symmetric $ extit{ extbf{p}}$-Laplacian systems with Orlicz-growth, advancing understanding of their regularity properties.

Contribution

It introduces novel second-order Caccioppoli estimates for evolutionary symmetric $ extit{ extbf{p}}$-Laplacian systems with Orlicz-growth, including the classical $p$-Laplacian case.

Findings

Derived spatial second-order Caccioppoli estimates for these systems

Results are new even for the classical $p$-Laplacian case

Advances regularity theory for nonlinear evolutionary PDEs

Abstract

We consider Orlicz-growth generalization to evolutionary $p$-Laplacian and to the evolutionary symmetric $p$-Laplacian. We derive the spatial second-order Caccioppoli estimate for a local weak solution to these systems. The result is new even for the $p$-case.