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Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem
We consider an obstacle-type problem Δu = f(x)χΩ�����in D, u = |∇u| = 0�����on D \ Ω, where D is a given open set in ℝn and Ω is an unknown open subset of D. The problem originates in potential theory, in connection with harmonic continuation of potentials. The qualitative …