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Register a new userA partially overdetermined problem in a half ball
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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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In this paper, we consider a partially overdetermined mixed boundary value problem in space forms. We generalize the main result in cite{GX} into the case of general domains with partial umbilical boundary in space forms. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is part of a geodesic ball.
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