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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…
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 comp…
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…
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…
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…
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…
On Gradient Flows with Obstacles and Euler's Elastica
Marius Müller
We examine a steepest energy descent flow with obstacle constraint in higher order energy frameworks where the maximum principle is not available. We construct the flow under gener…