Integrability and boundedness of solutions to some anisotropic problems

In this article, we give a series of results on the improved integrability and boundedness of solutions to several anisotropic problems. In particular, we consider the nonhomogeneous Dirichlet problem for anisotropic elliptic second-order equations. Moreover, we study anisotropic variational inequalities with unilateral and bilateral obstacles as well as gradient constraints. Finally, variational problems for integral functionals with anisotropic integrands are considered.