66 citations · 149 across the 23 of their papers we have counts for
Showing 2022 · math.APShow all
3 papers · 2 filters
math.AP2022★ 1 cited
Local minimizers of the interface length functional based on a concept of local paired calibrations
Julian Fischer, Sebastian Hensel, Tim Laux +1
We establish that regular flat partitions are locally minimizing for the interface energy with respect to perturbations of the phases. Regular flat partitions are partitions…
math.AP2022
Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow
Julian Fischer, Alice Marveggio
Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scalin…
math.AP2022
A monotonicity formula for minimizers of the Mumford-Shah functional in 2d and a sharp lower bound on the energy density
Julian Fischer
We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-…