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Publication 99-CNA-27
An Existence Result for a Nonconvex Variational Problem via Regularity Irene Fonseca Nicola Fusco Paolo Marcellini 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, not only adds significant technical difficulties, but also yields some unexpected phenomena. Get the paper in its entirety as |
