Tim Laux
Personal Homepage



Preprints
[19]     The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions,
with Julian Fischer, Sebastian Hensel, and Thilo Simon,
preprint.
arXiv:2003.05478
[18]     Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,
with Julian Fischer and Thilo Simon,
preprint.
arXiv:2002.11994
[17]     Mullins-Sekerka as the Wasserstein flow of the perimeter,
with Antonin Chambolle,
preprint.
arXiv:1910.02508
[16]     Implicit time discretization for the mean curvature flow of mean convex sets,
with Guido De Philippis,
to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5).
arXiv:1806.02716

Publications in Peer-Reviewed Journals
[15]     Well-posedness for degenerate elliptic PDE arising in optimal learning strategies,
with J. Miguel Villas-Boas,
Interfaces Free Bound., 22(1):119-129, 2020.
DOI: 10.4171/IFB/434
[14]     Brakke's inequality for the thresholding scheme,
with Felix Otto,
Calc. Var. Partial Differential Equations, 59(1):39-65, 2020.
DOI:10.1007/s00526-020-1696-8
[13]     Analysis of diffusion generated motion for mean curvature flow in codimension two: a gradient-flow approach,
with Aaron Yip,
Arch. Ration. Mech. Anal., 232(2):1113-1163, 2019.
DOI:10.1007/s00205-018-01340-x.
[12]     Convergence of the Allen-Cahn equation to multiphase mean curvature flow,
with Thilo M. Simon,
Comm. Pure Appl. Math., 71.8:1597-1647, 2018.
DOI:10.1002/cpa.21747
[11]     Gradient-flow techniques for the analysis of numerical schemes for multi-phase mean-curvature flow,
Geometric Flows, 3(1):76-89, 2018.
DOI:10.1515/geofl-2018-0006
[10]     The elastic flow of curves on the sphere,
with Anna Dall'Acqua, Chun-Chi Lin, Paola Pozzi, and Adrian Spener,
Geometric Flows, 3(1):1-13, 2018.
DOI:10.1515/geofl-2018-0001
[9]     Convergence of thresholding schemes incorporating bulk effects,
with Drew Swartz,
Interfaces Free Bound., 19(2):273-304, 2017.
DOI:10.4171/IFB/383
[8]      Convergence of the thresholding scheme for multi-phase mean-curvature flow,
with Felix Otto,
Calc. Var. Partial Differential Equations, 55(5):1-74, 2016.
DOI:10.1007/s00526-016-1053-0

Reports and Proceedings
[7]      A gradient-flow approach for the convergence of the anisotropic Allen-Cahn equation.
RIMS Kôkyûroku, Kyoto 2020.
[6]      The thresholding scheme for mean curvature flow and De Giorgi's ideas for minimizings movements,
with Felix Otto.
arXiv.1910.11442
[5]      Thresholding for mean curvature flow in codimension two,
Oberwolfach Report, 3/2019.
DOI:10.4171/OWR/2019/3
[4]      Kornwachstum in Polykristallen: Algorithmen für den mittleren Krümmungsfluss,
with Felix Otto,
Research Report, MPI for Mathematics in the Sciences, 2017.
Theses
[3]      Convergence of phase-field models and thresholding schemes via the gradient flow structure of multi-phase mean-curvature flow,
PhD Thesis, Max Planck Institute for Mathematics in the Sciences and University of Leipzig, 2017.
[2]      Dynamics of magnetic phase transitions,
Master's Thesis, RWTH Aachen University, 2013.
[1]      Maximum principles in differential inequalities and monotonicity of solutions,
Bachelor's Thesis, RWTH Aachen University, 2011.