In this talk we consider a new notion of variational capacity associated to the double-phase integrand and we work on domains whose complements are locally uniformly fat with respect to it. Under this assumption, we show an integral Hardy inequality and a global higher integrability result for quasi-minimizers of functionals of double-phase type, exploiting a self-improving property of this variational capacity and a Maz'ya type inequality related to the double-phase integrand.
This talk is based on a joint work with Leah Schätzler and Fabian Bäuerlein.