arXiv subjects
Publications and source records attributed to P. Dall'Aglio.
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous dependence with respect to data is discussed.
We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not depend on the components of the negative parts of the data which are concentrated on sets of capacity zero. The proof is based on a careful analysis of the behaviour of the potentials of two mutually singular measures near the points where both potentials tend to infinity.