Existence and regularity results for weak solutions to $(p,q)$-elliptic systems in divergence form

TL;DR

This paper establishes existence and regularity of weak solutions for nonlinear elliptic systems with $(p,q)$-growth, including higher differentiability results under specific conditions, advancing understanding of such systems.

Contribution

It provides new existence and regularity results for $(p,q)$-elliptic systems, especially achieving higher differentiability without dimension restrictions.

Findings

Proved existence of weak solutions under $(p,q)$-growth conditions.

Established higher differentiability results for solutions.

Achieved results without a dimension-dependent gap between $p$ and $q$.

Abstract

We prove existence and regularity results for weak solutions of non linear elliptic systems with non variational structure satisfying $(p,q)$-growth conditions. In particular we are able to prove higher differentiability results under a dimension-free gap between $p$ and $q$.