Inserted: 5 nov 2020
Last Updated: 5 nov 2020
Journal: Calculus of Variations and Partial Differential Equations
We consider overdetermined problems of Serrin's 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.