TWO-DIMENSIONAL VARIATIONAL PROBLEMS WITH A WIDE RANGE OF ANISOTROPY

摘要

We consider local minimizers u : R~2 (∩)Ω → R~M of the variational integral ∫H{▽u)dx Ω with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of V▽ and the differentiability of u in the classical sense. A Liouville type theorem is also established. Bibliography: 25 titles.