4 papers · 2 filters
Generic Mean Curvature Flow With Rough Weights
Fabius Krämer, Tim Laux, Keisuke Takasao
We prove the generic existence of mean curvature flows in spaces with rough weights. Our weak solutions are both unit-density Brakke flows and distributional solutions. Such a gene…
Strong Convergence of Continuous Median Filter Scheme
Fabius Krämer, Tim Laux
We introduce a continuous-time counterpart of the median filter that gradually denoises a given image. In the limit of vanishing stencil size, our results show that the evolution c…
Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
Tim Laux, Keisuke Takasao
Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cah…
The Verigin problem with phase transition as a Wasserstein flow
Anna Kubin, Tim Laux, Alice Marveggio
We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a…