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

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.

Keywords

• Elliptic system
• existence of solutions
• (p,q)-growth conditions
• regularity