Marcellini: An existence result for a nonconvex variational problem via regularity

Abstract. Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x-dependence, explicitly appearing in the integrands, adds signicant technical diculties in the proof. Mathematics Subject Classication. 49J45, 49K20, 35F30, 35R70. Received May 9, 2001