Isoperimetric cones and minimal solutions of partial overdetermined problems
Pacella, Filomena (Sapienza Università di Roma. Dipartimento di Matematica)
Tralli, Giulio (Università di Padova. Dipartimento d'Ingegneria Civile e Ambientale (DICEA))
Fecha: |
2021 |
Resumen: |
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 C1,1 -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]. |
Derechos: |
Tots els drets reservats. |
Lengua: |
Anglès |
Documento: |
Article ; recerca ; Versió publicada |
Materia: |
Isoperimetric cones ;
Mixed boundary value problems ;
Constant mean curvature polar graphs ;
Torsional rigidity problems |
Publicado en: |
Publicacions matemàtiques, Vol. 65 Núm. 1 (2021) , p. 61-81 (Articles) , ISSN 2014-4350 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/383647
DOI: 10.5565/PUBLMAT6512102
DOI: 10.5565/publicacionsmatematiques.v65i1.383647
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