Tim Laux | Publications

Preprints

30.   Quantitative convergence of the nonlocal Allen-Cahn equation to volume-preserving mean curvature flow,
with Milan Krömer,
preprint, 14 pp.
arXiv:2309.12409
29.   Generic levelsets in mean curvature flow are BV solutions,
with Anton Ullrich,
submitted, 16 pp.
arXiv:2301.01097
28.   A uniqueness and stability principle for surface diffusion,
with Milan Krömer,
submitted, 26 pp.
arXiv:2212.12487
27.   Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow,
with Kerrek Stinson and Clemens Ullrich,
submitted, 62 pp.
arXiv:2212.11939
26.   Local minimizers of the interface length functional based on a concept of local paired calibrations,
with Julian Fischer, Sebastian Hensel, and Theresa M. Simon,
submitted, 35 pp.
arXiv:2212.11840
25.

 

Large data limit of the MBO scheme for data clustering: Convergence of the dynamics,
with Jona Lelmi,
submitted, 50 pp.
arxiv:2209.05837
24.   A phase-field version of the Faber-Krahn theorem,
with Paul Hüttl and Patrik Knopf,
submitted, 30 pp.
arXiv:2207.10946
23.   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
22.   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
21.      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,
short version in (minor) revision at J. Eur. Math. Soc., 104 pp.
arXiv:2003.05478

Publications in Peer-Reviewed Journals

20.   Sharp interface limit of the Cahn-Hilliard reaction model for lithium-ion batteries,
with Kerrek Stinson,
to appear in Math. Models Methods Appl. Sci., 20 pp.
arXiv:2209.07380
19.   Phase-field methods for spectral shape and topology optimization,
with Harald Garcke, Paul Hüttl, Christian Kahle, and Patrik Knopf,
ESAIM: Control Optim. Calc. Var. 29:10, 57 pp., 2023.
DOI:10.1051/cocv/2022090
18.   Strong convergence of the thresholding scheme for the mean curvature flow of mean convex sets,
with Jakob Fuchs,
Adv. Calc. Var. (online first), 59 pp.
DOI:10.1515/acv-2022-0020
17.   Weak-strong uniqueness for volume-preserving mean curvature flow,
Rev. Mat. Iberoam. (online first), 18 pp.
DOI:10.4171/RMI/1395
16.   The Hele-Shaw flow as the sharp interface limit of the Cahn-Hilliard equation with disparate mobilities,
with Milan Krömer,
Comm. Partial Differential Equations, 47(12):2444-2486, 2022.
DOI: 10.1080/03605302.2022.2129384
15.   BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness,
with Sebastian Hensel,
Indiana Univ. Math. J. (online first), 24 pp.
arXiv.2112.11150
14.   Weak-strong uniqueness for the mean curvature flow of double bubbles,
with Sebastian Hensel,
Interfaces Free Bound. 25, no. 1, pp. 37–107, 2023.
DOI:10.4171/IFB/484
13.   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, 42 pp., 2022.
DOI:10.1007/s00526-021-02146-8
12.   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
11.      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
10.      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
9.      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
8.      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
7.      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
6.      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
5.      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
4.      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
3.      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
2.      Convergence of thresholding schemes incorporating bulk effects,
with Drew Swartz,
Interfaces Free Bound., 19(2):273-304, 2017.
DOI:10.4171/IFB/383
1.      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

P7.   A new varifold solution concept for mean curvature flow,
with Sebastian Hensel,
Oberwolfach Report (to appear), 2023.
P6.   Large data limit of the MBO scheme for data clustering,
with Jona Lelmi,
Proc. Appl. Math. Mech. 22.1, e202200308, 2023.
DOI:10.1002/pamm.202200308
P5.      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. 
P4.      The thresholding scheme for mean curvature flow and De Giorgi's ideas for minimizing 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.
P3.       Thresholding for mean curvature flow in codimension two,
with Aaron Yip,
Oberwolfach Report, OWR 3/2019, pp. 147-150.
DOI:10.4171/OWR/2019/3
P2.   Brakke – de Giorgi – Osher,
with Felix Otto,
Oberwolfach Report, OWR 54/2017, pp. 3219-3222.
DOI:10.4171/OWR/2017/54
P1.      Kornwachstum in Polykristallen: Algorithmen für den mittleren Krümmungsfluss,
with Felix Otto,
Research Report, MPI for Mathematics in the Sciences, 2017.

Lecture Notes

L1.      Distributional solutions to mean curvature flow, 38 pages,
arXiv:2108.08347

Outreach

O2.   Die Mathematik des Kristallwachstums – ein Forschungsauftrag für Schüler*innen,
with Fabian Weidt and Stefan Hartmann
Exposition, lecture material for highschool teachers & a game
O1.   Optimale Formen und Muster - Ist die Natur eine Mathematikerin?
Vorlesung im Rahmen der Schüler*innenwoche am Hausdorffzentrum für Mathematik der Universität Bonn
Skript mit Aufgaben

Theses

T3.      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.
T2.      Dynamics of magnetic phase transitions,
Master's Thesis, RWTH Aachen University, 2013.
T1.      Maximum principles in differential inequalities and monotonicity of solutions,
Bachelor's Thesis, RWTH Aachen University, 2011.

 

Contact

Managing Director: Prof. Dr. Juan J. L. Velázquez
Chief Administrator: Dr. B. Doerffel
geschaeftsfuehrung@iam.uni-bonn.de
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Mailing address

Institute for Applied Mathematics
University of Bonn
Endenicher Allee 60
D-53115 Bonn / Germany