6 papers
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…
Classification and stability of penalized pinned elasticae
Marius Müller, Kensuke Yoshizawa
This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit…
A nongraphical obstacle problem for elastic curves
Marius Müller, Kensuke Yoshizawa
We study an obstacle problem for the length-penalized elastic bending energy for open planar curves pinned at the boundary. We first consider the case without length penalization a…
Lipschitz regularity for -harmonic interface transmission problems
Marius Müller
We prove optimal Lipschitz regularity for weak solutions of the measure-valued -Poisson equation . Here , is a c…
An anisotropic Alt-Caffarelli problem of higher order
Marius Müller
We study a higher order version of the Alt-Caffarelli problem in two dimensions, where the Dirichlet energy is replaced by an anisotropic bending energy. This extends a previous st…
Dimension reduction for Willmore flows of tori: fixed conformal class and analysis of singularities
Anna Dall'Acqua, Marius Müller, Fabian Rupp +1
This work studies Willmore flows of tori and their singularities via a dimension reduction approach. We introduce a Willmore flow that preserves the degenerate constraint of prescr…