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].
Citation
Filomena Pacella. Giulio Tralli. "Isoperimetric cones and minimal solutions of partial overdetermined problems." Publ. Mat. 65 (1) 61 - 81, 2021. https://doi.org/10.5565/PUBLMAT6512102
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