Unilateral problems with measure data: links and convergence

Abstract

We deal with an obstacle problem with measure data. We improve our previous result of existence in a form which permits us to obtain a convergence result with respect to Mosco convergence of obstacles and uniqueness of the solution in the case where the measure data vanishes on sets of zero capacity. We also give a property, which is analogous, for renormalized solutions, to a recent characterization obtained in [10].