Obstacle Problems for Green Potentials and for Parabolic Quasiminima

Abstract: The thesis consists of two parts. In the first part pure potential theoretic methods are employed to study the obstacle problem connected with a uniformly elliptic second-order differential operator in divergence form. Regular points of the obstacles are characterized by the classical Wiener criterion. The second part deals with a class of functions satisfying a certain integral inequality. A prototype for this function class is the class of subsolutions (or, more generally) the class of sub-quasiminima, associated to a degenerate nonlinear parabolic differential operator and to a couple of irregular obstacles. A sufficient condition on the obstacles for regularity of a point is given.