Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures

Abstract

We consider the homogeneous Dirichlet problem (1.1) with f ∈ M(Ω), the space of Radon measures and Ω open bounded set of IRN . For f "∈ H−1(Ω), some weak solutions have been introduced: we show that the one of Boccardo-Gallou¨et and the one of Stampacchia are the same. Then we show, with a counter-example of Serrin that the weak formulation of the first one does not ensure uniqueness.

Keywords

• uniqueness
• elliptic equation
• non variational framewor