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

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

Information

Received: 3 June 2019; Published: 2021
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185827
Digital Object Identifier: 10.5565/PUBLMAT6512102

Subjects:
Primary: 49Q10
Secondary: 35B06 , 35N25 , 53A10 , 74G50

Keywords: constant mean curvature polar graphs , isoperimetric cones , mixed boundary value problems , torsional rigidity problems

Rights: Copyright © 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.65 • No. 1 • 2021
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