Tim Laux | Publications

Preprints

[29]   Weak-strong uniqueness for volume-preserving mean curvature flow,
submitted, 14 pp.
arXiv:2205.13040
[28]   Strong convergence of the thresholding scheme for the mean curvature flow of mean convex sets,
with Jakob Fuchs,
submitted, 55 pp.
arxiv:2201.00413
[27]   BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness,
with Sebastian Hensel,
in (minor) revision at Indiana Univ. Math. J., 24 pp.
arXiv.2112.11150
[26]   Large data limit of the MBO scheme for data clustering: Γ-convergence of the thresholding energies,
with Jona Lelmi,
submitted, 57 pp.
arXiv:2112.06737
[25]   The Hele-Shaw flow as the sharp interface limit of the Cahn-Hilliard equation with disparate mobilities,
with Milan Krömer,
in (minor) revision at Comm. Partial Differential Equations, 46 pp.
arxiv:2111.14505
[24]   A new varifold solution concept for mean curvature flow: convergence of the Allen-Cahn equation and weak-strong uniqueness,
with Sebastian Hensel,
submitted, 38 pp.
arXiv:2109.04233
[23]   Weak-strong uniqueness for the mean curvature flow of double bubbles,
with Sebastian Hensel,
accepted for publication in Interfaces Free Bound., 59 pp.
arXiv:2108.01733
[22]      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 Theresa M. Simon,
submitted, 104 pp.
arXiv:2003.05478

Publications in Peer-Reviewed Journals

[21]   De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions,
with Jona Lelmi,
Calc. Var. Partial Differential Equations, 61(1):35, 42pp., 2022.
DOI:10.1007/s00526-021-02146-8
[20]   Nematic-isotropic phase transition in liquid crystals: a variational derivation of effective geometric motions,
with Yuning Liu,
Arch. Ration. Mech. Anal. 241(3):1785-1814, 2021.
DOI:10.1007/s00205-021-01681-0
[19]      Convergence rates of the Allen-Cahn equation to mean curvature flow: a short proof based on relative entropies,
with Julian Fischer and Theresa M. Simon,
SIAM J. Math. Anal., 52(6), 6222-6233, 2020.
DOI:10.1137/20M1322182
[18]      Mullins-Sekerka as the Wasserstein flow of the perimeter,
with Antonin Chambolle,
Proc. Amer. Math. Soc., 149(7):2943-2956, 2021.
DOI:10.1090/proc/15401
[17]      Implicit time discretization for the mean curvature flow of mean convex sets,
with Guido De Philippis,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 21:911-930, 2020.
DOI:10.2422/2036-2145.201810_003
[16]      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
[15]      Brakke's inequality for the thresholding scheme,
with Felix Otto,
Calc. Var. Partial Differential Equations, 59(1):39, 26 pp., 2020.
DOI:10.1007/s00526-020-1696-8
[14]      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
[13]      Convergence of the Allen-Cahn equation to multiphase mean curvature flow,
with Theresa M. Simon,
Comm. Pure Appl. Math., 71.8:1597-1647, 2018.
DOI:10.1002/cpa.21747
[12]      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
[11]      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
[10]      Convergence of thresholding schemes incorporating bulk effects,
with Drew Swartz,
Interfaces Free Bound., 19(2):273-304, 2017.
DOI:10.4171/IFB/383
[9]       Convergence of the thresholding scheme for multi-phase mean-curvature flow,
with Felix Otto,
Calc. Var. Partial Differential Equations, 55(5):129, 74 pp., 2016.
DOI:10.1007/s00526-016-1053-0

Reports and Proceedings

[8]       A gradient-flow approach for the convergence of the anisotropic Allen-Cahn equation.
RIMS Kôkyûroku 2172, Geometric Aspects of Solutions to Partial Differential Equations, pp. 32-42, Research Institute for Mathematical Sciences, Kyoto University, Japan, 2020. 
[7]       The thresholding scheme for mean curvature flow and De Giorgi's ideas for minimizings movements,
with Felix Otto,
Adv. Stud. Pure Math. 85, The Role of Metrics in the Theory of Partial Differential Equations, pp. 63-93, Mathematical Society of Japan, 2020.
[6]       Thresholding for mean curvature flow in codimension two,
Oberwolfach Report, 3/2019.
DOI:10.4171/OWR/2019/3
[5]       Kornwachstum in Polykristallen: Algorithmen für den mittleren Krümmungsfluss,
with Felix Otto,
Research Report, MPI for Mathematics in the Sciences, 2017.

Lecture Notes

[4]       Distributional solutions to mean curvature flow, 38 pages,
arXiv:2108.08347

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.

 

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