Variational problems with obstacles and integral constraints

Various problems in mathematics and physics can be formulated in terms of a variational problem with obstacles and integral constraints, e.g. finding a surface of minimal area with prescribed volume in a bounded region.We are concerned with the regularity of solutions of variational problems: We show that the minima of a variational integral under all Sobolewfunctions with prescribed boundary values, lying between two obstacles, and fulfilling some integral constraints, are bounded and Hölder-continuous. We do not assume any differentiability or convexity of the integrand, but only a Caratheodory and a growth condition.This research has been supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft.