ﻻ يوجد ملخص باللغة العربية
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.
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 wh
In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for non-quasiana
We prove a rigidity result for the anisotropic Laplacian. More precisely, the domain of the problem is bounded by an unknown surface supporting a Dirichlet condition together with a Neumann-type condition which is not translation-invariant. Using a c
We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function $P$ and integral identities. In dimension $2$, we pr
We consider overdetermined problems of Serrins type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector.