Existence results for hemivariational inequalities with measures

Abstract

We prove existence results for multivalued quasilinear elliptic problems of hemivariational inequality type with measure data right-hand sides. In case of L ¹-data, we study existence and enclosure behaviors of solutions by an appropriate sub-supersolution approach. The proofs of our results are based on general existence theory for multivalued pseudomonotone operators, and approximation-, truncation-, and special test function techniques.

Keywords:

• Quasilinear elliptic inclusion
• Hemivariational inequality
• Radon-measure
• L ¹-data
• Clarke's generalized gradient
• Multivalued pseudomonotone operators