Calculus of variations in the anisotropic setting.

In this talk, we will review some recent results concerning existence and regularity of minimizers of anisotropic variational problems. The anisotropy that we have in mind concerns different orders of derivation in different directions, thus we work with differential operators that need not be homogeneous in the usual sense. We will explain how to obtain existence and regularity statements for minimizers of such problems using the usual tools of the calculus of variations (such as quasiconvexity) combined with the structural theory of anisotropic Sobolev spaces and regularity theory for linear quasielliptic equations. This talk is based on my on-going collaboration with my doctoral advisor Prof. Jan Kristensen.