Optimality of smallness conditions in Willmore obstacle problems under Dirichlet boundary conditions
Hans-Christoph Grunau, Shinya Okabe · Nonlinear Analysis Real World Applications · 2025
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.