Global improved differentiability for minimisers of (p,q)-functionals

I will give an overview of some regularity results for minimisers of (p,q)-functionals, which are a class of functionals arising in nonlinear elasticity and other applications. A particular focus will be on the use of the difference quotient method to obtain global improved (Sobolev-)differentiability results. Further, I will discuss the occurrence of the Lavrentiev phenomenon in the case of non-autonomous integrands.