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A partially overdetermined problem in a half ball (1807.01507v3)
Published 4 Jul 2018 in math.AP
Abstract: In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap intersecting $\ss{n-1}$ orthogonally. As an application, we show a stationary point for a partially torsional rigidity under a volume constraint must be a spherical cap.
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