Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones
- In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of nonradial minimizers, under a volume constraint, of the associated torsional energy functional. In particular we give a condition on the domain D on the sphere spanning the cone which ensures that the spherical sector is not a minimizer. Similar results are obtained for the relative isoperimetric problem in nonconvex cones.
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| Author: | Alessandro Iacopetti, Filomena PacellaORCiDGND, Tobias WethORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-694532 |
| DOI: | https://doi.org/10.1007/s00205-022-01801-4 |
| ISSN: | 1432-0673 |
| Parent Title (English): | Archive for rational mechanics and analysis |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2022/06/21 |
| Date of first Publication: | 2022/06/21 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2023/01/10 |
| Volume: | 245 |
| Issue: | 2 |
| Page Number: | 54 |
| First Page: | 1005 |
| Last Page: | 1058 |
| Note: | Open access funding provided by Universitá degli Studi di Roma La Sapienza within the CRUI-CARE Agreement. |
| Note: | Research partially supported by Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
