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arXiv · 1905.10139

Isoperimetric cones and minimal solutions of partial overdetermined problems

Filomena Pacella·Giulio Tralli
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Abstract

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a torsional energy functional are spherical sectors centered at the vertex of the cone. We also show that cones close in the $C^{1,1}$-metric to an isoperimetric one are also isoperimetric, generalizing so a result of [1]. This is achieved by using a characterization of constant mean curvature polar graphs in cones which improves a result of [18].

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Filomena Pacella, Giulio Tralli. 2019-05-24. Isoperimetric cones and minimal solutions of partial overdetermined problems. https://arxiv.org/abs/1905.10139

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