Some properties of the solutions of obstacle problems with measure data

2000/06/02 by P. Dall'Aglio, G. Dal Maso
Mathematics · #math.FA

paper · pdf

published as Ricerche Mat. 48 (1999) Suppl. 99-116 · 18 pages

arxiv created 2000/06/02 · arxiv updated 2009/11/30

Abstract

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.

Related

• Obstacles problems with measure data
• Stability results for solutions of obstacle problems with measure data
• On global solutions of the obstacle problem
• Singular elliptic measure data problems with irregular obstacles
• The structure of the regular part of the free boundary close to singularities in the obstacle problem