4 papers
Euler's elastica functional as a large mass limit of a two-dimensional non-local isoperimetric problem
Cyrill B. Muratov, Matteo Novaga, Theresa M. Simon
We consider a large mass limit of the non-local isoperimetric problem with a repulsive Yukawa potential in two space dimensions. In this limit, the non-local term concentrates on t…
Existence of higher degree minimizers in the magnetic skyrmion problem
Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov
We demonstrate existence of topologically nontrivial energy minimizing maps of a given positive degree from bounded domains in the plane to in a variational model des…
On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation
Angkana Rüland, Theresa M. Simon
We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple lamin…
Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
Julian Fischer, Tim Laux, Theresa M. Simon
We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter…