Existence and uniqueness of solutions for nonlinear obstacle problems with measure data
This paper deals with obstacle problems with measure data associated to a nonlinear elliptic differential operator of monotone type, mapping \(W^{1,p}_0(\Omega)\), \(p>1\), into \(W^{-1,p'}(\Omega)\). The author considers as data bounded Radon measures vanishing on sets of capacity zero and introduce a definition of ``entropy'' solution for obstacle problems ``similar'' to the characterization given by Kinderlehrer and Stampacchia for data in \(W^{-1,p'}(\Omega)\). The existence of such a solution is proved by an approximation technique, the uniqueness is implicit in the definition. The found solution is characterized by the complementarity system and a stability result with respect to a strong convergence is proved.
scientific article; zbMATH DE number 1545351