Dr. Simon Eberle

CV, Publications

​​​​Dr. Simon Eberle

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​​       Dr. Simon Eberle
       AG Analysis of Partial Differential Equations
       University of Duisburg-Essen
       Thea-Leymann-Straße 9
       D-45127 Essen
       E-mail: simon.eberle[at]uni-due.de

 

 

Research
  • regularity of the free boundary in the obstacle problem
  • global solutions of the obstacle / thin obstacle problem
  • Wasserstein gradient flows
  • non-periodic homogenization
  • traveling waves in non-homogeneous media or genometries and their long-term asympotics
Curriculum Vitae CV.pdf
Publications

Preprints:

• Simon Eberle, Arnulf Jentzen, and Georg S. Weiss. Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation. Submitted 2021. [ arXiv ]
• Simon Eberle, Henrik Shahgholian, and Georg S. Weiss. On global solutions of the obstacle problem -- application to the local analysis close to singularities. Submitted, 2021. [ arXiv ]

Published:

8 Simon Eberle, Xavier Ros-Oton, and Georg S. Weiss. Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional laplacian. Nonlinear Analysis. Theory, Methods & Application, 211, 2021. [ DOI ]
7 Simon Eberle. Front blocking versus propagation in the presence of drift term varying in the direction of propagation. Nonlinear Analysis. Theory, Methods & Application, 176, 2018. [ DOI ]
6 Simon Eberle and Georg Sebastian Weiss. Characterizing compact coincidence sets in the obstacle problem -- a short proof. St. Petersburg Mathematical Journal, Special issue dedicated to 85th anniversary of outstanding Russian mathematician Prof. Nina N. Uraltseva, 32, 2020. [ DOI ]
5 Simon Eberle. Front blocking in the presence of gradient drift. Journal of Differential Equations, 267(12), 2019. [ DOI ]
4 Simon Eberle. A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities in a channel with decreasing cross section. Nonlinear Analysis, 172, 2018. [ DOI ]
3 Simon Eberle. A heteroclinic orbit connecting traveling waves pertaining to different nonlinearities. Journal of Differential Equations, 265(3), 2018. [ DOI ]
2 Simon Eberle, Barbara Niethammer, and André Schlichting. Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation. Nonlinear Analysis, 158, 2017. [ DOI ]
1 Simon Eberle. Explicit formulas for homogenization limits in certain non-periodic problems including ramified domains. ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 96(10), 2016. [ DOI ]

Miscellaneous:

• Simon Eberle and Peter Lewintan. Ein Vorschlag zur konsistenten Einführung der Ableitung mit der Zoom-in-Methode. Mathematische Semesterberichte, 66, 2019. [ DOI ]
• Simon Eberle and Georg S. Weiss. Wellen und Fronten in der Mathematik. UNIKATE (Journal of the University of Duisburg-Essen), 53, 2019. [ PDF ]
Dissertation On global solutions of the obstacle problem