An existence theorem for set differential inclusions in a semilinear metric space
An optimal control problem for an elliptic variational inequality
Approximation methods for nonlinear problems with constraints in form of variational inequalities
Approximations by regular sets and Wiener solutions in metric spaces
Let be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for -harmonic functions and to show that they coincide with three other notions of generalized solutions.