188 citations · 282 across the 13 of their papers we have counts for
21 papers
Localization properties of a free boundary problem for cell polarization
B. Niethammer, M. Röger, J. J. L. Velázquez
We investigate localization in a time-dependent contrained obstacle problem for the density of an active protein on a cell membrane. This free boundary problem has been derived in…
Mathematical analysis of a mesoscale model for multiphase membranes
Jakob Fuchs, Matthias Röger
In this paper we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author [Ar…
Phase separation on varying surfaces and convergence of diffuse interface approximations
Heiner Olbermann, Matthias Röger
In this paper we consider phase separations on (generalized) hypersurfaces in Euclidian space. We consider a diffuse surface area (line tension) energy of Modica-Mortola type and p…
"Gradient-free" diffuse approximations of the Willmore functional and Willmore flow
Nils Dabrock, Sascha Knüttel, Matthias Röger
We introduce new diffuse approximations of the Willmore functional and the Willmore flow. They are based on a corresponding approximation of the perimeter that has been studied by…
Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphs
Nils Dabrock, Martina Hofmanová, Matthias Röger
We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. We establish existence of martingale solutions which are strong in t…
Quantitative estimates for bending energies and applications to non-local variational problems
Michael Goldman, Matteo Novaga, Matthias Röger
We discuss a variational model, given by a weighted sum of perimeter, bending and Riesz interaction energies, that could be considered as a toy model for charged elastic drops. The…