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.
Serrin’s type overdetermined problems in convex cones / G. Ciraolo, A. Roncoroni. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 59:1(2020), pp. 28.1-28.21. [10.1007/s00526-019-1678-x]
Serrin’s type overdetermined problems in convex cones
G. Ciraolo
;
2020
Abstract
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.
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