The Obstacle Problem
In this chapter, we start studying the question of minimizing the energy Gε and we prove the main result of Γ-convergence of Gε. As already mentioned, configurations have a vorticity μ(uε,Aε), which, according to Chapter 6, is compact as ε → 0 (under a suitable energy bound) and the result we obtain below shows that minimizers of Gε have vorticities which converge to a measure which minimizes a certain convex energy. This measure, by convex duality, is shown to be the solution to a simple obstacle problem.
KeywordsVariational Inequality Radon Measure Obstacle Problem Unique Minimizer Smooth Bounded Domain
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