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Abstract: The characterization of global solutions to the obstacle problem in R^N, or equivalently of null quadrature domains, has been studied over more than 90 years. In this paper we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.

Seminar website: https://sites.math.rutgers.edu/~yyli/NonlinearAnalysisSeminar.html