Publications

Preprints

1. Complete classification of global solutions to the obstacle problem (with Alessio Figalli and Georg S. Weiss),

45 pages. 2022, arXiv

2. Normalized gradient flow optimization in the training of ReLU artificial neural networks (with Arnulf Jentzen, Adrian Riekert and Georg S. Weiss),

26 pages, 2022, arXiv

3. The structure of the regular part of the free boundary close to singularities in the obstacle problem (with Henrik Shahgholian and Georg S. Weiss),

11 pages, 2022, arXiv

4. Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation (with Arnulf Jentzen, Adrian Riekert and Georg S. Weiss),

30 pages, 2021, arXiv

5. On global solutions of the obstacle problem (with Henrik Shahgholian and Georg S. Weiss),

28 pages, 2020, arXiv, accepted by Duke Mathematical Journal

Published

1. Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional Laplacian (with Xavier Ros-Oton and Georg S. Weiss),

Nonlinear Analysis, 7 pages, 2021, arXiv

2. Front blocking versus propagation in the presence of a drift term varying in the direction of propagation,

Nonlinear Analysis, 21 pages, 2020, arXiv

3. Characterizing compact coincidence sets in the obstacle problem---a short proof (with Georg S. Weiss),

Algebra i Analiz, 7 pages, 2020, arXiv

4. Front blocking in the presence of gradient drift,

Journal of Differential Equations, 13 pages, 2019, arXiv

5. A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities in a channel with decreasing cross section,

Nonlinear Analysis, 16 pages, 2018

6. A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities,

Journal of Differential Equations, 26 pages, 2018, arXiv

7. Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation (with Barbara Niethammer and André Schlichting),

Nonlinear Analysis, 27 pages, 2017, arXiv

8. Explicit formulas for homogenization limits in certain non-periodic problems including ramified domains,

Journal for Applied Mathematics and Mechanics (ZAMM), 15 pages, 2016

PhD thesis: On global solutions of the obstacle problem