LAUSR

Abstract: We consider a two-obstacle problem with measure data. For measures that do not charge sets of zero p(·)capacity, we obtain the existence and uniqueness of the solution. On the other hand, for the measure concentrated on a set with zero p(·)-capacity, we prove a nonexistence result in the sense that when one looks for solutions via approximation, one cannot find a reasonable solution; see Theorem 2.3 and Remark 2.1 below.