An obstacle problem for the p-elastic energy
- In this paper we consider an obstacle problem for a generalization of the p-elastic energy among graphical curves with fixed ends. Taking into account that the Euler–Lagrange equation has a degeneracy, we address the question whether solutions have a flat part, i.e. an open interval where the curvature vanishes. We also investigate which is the main cause of the loss of regularity, the obstacle or the degeneracy. Moreover, we give several conditions on the obstacle that assure existence and nonexistence of solutions. The analysis can be refined in the special case of the p-elastica functional, where we obtain sharp existence results and uniqueness for symmetric minimizers.
| Author: | Anna Dall'Acqua, Marius MüllerGND, Shinya Okabe, Kensuke Yoshizawa |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1139146 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/113914 |
| ISSN: | 0944-2669OPAC |
| ISSN: | 1432-0835OPAC |
| Parent Title (English): | Calculus of Variations and Partial Differential Equations |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2024/07/09 |
| Volume: | 63 |
| Issue: | 6 |
| First Page: | 145 |
| DOI: | https://doi.org/10.1007/s00526-024-02752-2 |
| 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 |
