Optimality of smallness conditions in Willmore obstacle problems under Dirichlet boundary conditions
We consider the obstacle problem under Dirichlet boundary conditions for Euler’s elastica functional in the class of one-dimensional symmetric graphs over the real axis. We prove the optimality of a previously obtained smallness condition on the size of obstacles such that the obstacle problem possesses a minimiser.
Authors
- Hans-Christoph Grunau (ORCID: https://orcid.org/0000-0002-5343-1934)
- Shinya Okabe (ORCID: https://orcid.org/0000-0003-0103-7449)
Institutions
- Tohoku University (JP)
- Otto-von-Guericke-Universität Magdeburg (DE)
Publication Details
- Journal
- Nonlinear Analysis Real World Applications
- Published
- 2025-03-14
- DOI
- https://doi.org/10.1016/j.nonrwa.2025.104363
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Japan Society for the Promotion of Science