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Regular Curves, Singular Graphs: Cantor Parts and the Relaxed Willmore Energy
Hans-Christoph Grunau, Boris Gulyak
The authors construct a continuous BV function whose derivative contains a non‑zero Cantor part while its relaxed one‑dimensional Willmore energy remains finite, demonstrating that…
Global minimizers for a two-sided biharmonic Alt-Caffarelli problem
Hans-Christoph Grunau, Marius Müller
We study global minimizers of biharmonic analogues of the Alt-Caffarelli functional. It turns out that half-space solutions are global minimizers for the two-sided Alt-Caffarelli f…
On the basin of attraction for the free boundary free elastic flow
Klaus Deckelnick, Hans-Christoph Grunau, Robert Nürnberg +2
The free boundary free elastic flow is the steepest descent gradient flow for the elastic energy of curves meeting parallel lines perpendicularly. In this article we prove that the…
Willmore obstacle problems under Dirichlet boundary conditions
Hans-Christoph Grunau, Shinya Okabe
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…
A biharmonic analogue of the Alt-Caffarelli problem
Hans-Christoph Grunau, Marius Müller
We study a natural biharmonic analogue of the classical Alt-Caffarelli problem, both under Dirichlet and under Navier boundary conditions. We show existence, basic properties and $…