• Corpus ID: 232404433

Willmore obstacle problems under Dirichlet boundary conditions

@inproceedings{Grunau2021WillmoreOP,
  title={Willmore obstacle problems under Dirichlet boundary conditions},
  author={Hans-Christoph Grunau and Shinya Okabe},
  year={2021}
}
. We consider obstacle problems for the Willmore functional in the class of graphs of functions and surfaces of revolution with Dirichlet boundary conditions. We prove the existence of minimisers of the obstacle problems under the assumption that the Willmore energy with the unilateral constraint is below a universal bound. We address the question whether such bounds are necessary in order to ensure the solvability of the obstacle problems. Moreover, we give several instructive examples of… 
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