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 posse...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 85; p. 104363
Main Authors Grunau, Hans-Christoph, Okabe, Shinya
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.10.2025
Subjects
Dirichlet boundary conditions
Elastic energy
Obstacle problem
Optimality
Smallness condition
secondary
Elastic energy
Dirichlet boundary conditions
Optimality
Smallness condition
primary
Obstacle problem
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Summary: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.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2025.104363