The biharmonic Alt–Caffarelli problem in 2D
- We examine a variational free boundary problem of Alt–Caffarelli type for the biharmonic operator with Navier boundary conditions in two dimensions. We show interior C2-regularity of minimizers and that the free boundary consists of finitely many C2-hypersurfaces. With the aid of these results, we can prove that minimizers are in general not unique. We investigate radial symmetry of minimizers and compute radial solutions explicitly.
| Author: | Marius MüllerGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1283000 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/128300 |
| ISSN: | 0373-3114OPAC |
| ISSN: | 1618-1891OPAC |
| Parent Title (English): | Annali di Matematica Pura ed Applicata (1923 -) |
| Publisher: | Springer Science and Business Media LLC |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2022 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2026/02/20 |
| Volume: | 201 |
| Issue: | 4 |
| First Page: | 1753 |
| Last Page: | 1799 |
| DOI: | https://doi.org/10.1007/s10231-021-01178-3 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
