Existence and regularity results for weak solutions to $(p,q)$-elliptic   systems in divergence form
  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 $q$. 
Miroslav Bul\'i\v{c}ek, Giovanni Cupini, Bianca Stroffolini and Anna   Verde
math.AP