Optimizing solutions with competing anisotropic (p, q)-Laplacian in hemivariational inequalities

For differential inclusions and hemivariational inequalities driven by anisotropic differential operators, we establish the existence of generalized variational solutions and weak solutions. The main novelty consists in allowing that the driving operators might not satisfy any ellipticity condition, which is achieved for the first time in the anisotropic and nonsmooth context. The approach is based on a finite dimensional approximation process.