Prof. Dr. G. S. Weiss

• CV • Publications

​Photo Weiss

​​      Prof. Dr. G. S. Weiss
       AG Analysis of Partial Differential Equations
       University of Duisburg-Essen
       Thea-Leymann-Straße 9
       D-45127 Essen
       E-mail: georg.weiss[at]uni-due.de

 

 

Research
  • free boundary problems in ElectroHydroDynamic equations
  • the geometry of uniformly rotating relativistic stars
  • traveling waves in ramified domains
  • biharmonic free boundary problems
     
Curriculum Vitae

Work experience:

11/1991 - 03/1995 Research Assistant at the Institute for Applied Mathematics, University of Bonn
04/1995 - 03/1996 JSPS/Humboldt-Fellow at Chiba University, Japan
04/1996 - 03/2000 Assistant Professor (permanent position), Department of Mathematics, Tokyo Institute of Technology, Japan
04/2000 - 04/2005 Associate Professor (permanent position), Graduate School of Mathematical Sciences, University of Tokyo, Japan
04/2005 - 09/2005 Max-Planck fellowship at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
10/2005 - 09/2010 continuing the position as Associate Professor, University of Tokyo, Japan
in 2010 two offers of full professor positions (Leipzig and Düsseldorf)
10/2010 - 09/2014 full professor at the Heinrich Heine University in Düsseldorf
since 10/2014 full professor at the University of Duisburg-Essen
10/2020-10/2022 Dean of the Faculty of Mathematics, University of Duisburg-Essen

Education:

10/1991 Diplom, University of Bonn
07/1993 PhD, University of Bonn

 
Publications:

  1. Preprints:

    • Simon Eberle, Alessio Figalli and Georg S. Weiss. Complete classification of global solutions to the obstacle problem. Accepted for publication in the Annals of Mathematics, 2024. [ Ann. Math. ]
      Dennis Kriventsov and Georg S. Weiss. Rectifiability, finite Hausdorff measure, and compactness for non-minimizing Bernoulli free boundaries. Accepted for publication in Communications on Pure and Applied Mathematics (2024). [ arXiv ]
    • Anthony Salib and Georg S. Weiss. A singular perturbation approach to the Dirichlet-area minimisation problem. Submitted 2024. [ arXiv ]
    • Anthony Salib and Georg S. Weiss. Classification of global solutions to the obstacle problem in the plane Submitted 2024. [ arXiv ]
    • Simon Eberle, Arnulf Jentzen, Adrian Riekert, and Georg S. Weiss. Normalized gradient flow optimization in the training of ReLU artificial neural networks. Submitted 2022. [ arXiv ]

    Published:

    56 Simon Eberle, Henrik Shahgholian and Georg S. Weiss. The structure of the regular part of the free boundary close to singularities in the obstacle problem. Journal of Differential Equations, 377, 2023. [ Journal of Differential Equations ]
    55 Simon Eberle, Henrik Shahgholian and Georg S. Weiss. On global solutions of the obstacle problem. Duke Mathematical Journal, 172, 2023. [ Duke Mathematical Journal ]
    54 Simon Eberle, Arnulf Jentzen, Adrian Riekert, and Georg S. Weiss. Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation. Electronic Research Archive. Special Issue on Dynamics, Control and Applications of Discontinuous Differential Systems, 31, 2023 [ AIMS Press ]
    53 Gohar Aleksanyan, Morteza Fotouhi, Henrik Shahgholian and Georg S. Weiss. Regularity of the free boundary for a parabolic cooperative system. Calculus of Variations and Partial Differential Equations, 61, 2022. [ DOI ]
    52 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 ]
    51 Morteza Fotouhi, Andreas Minne, Henrik Shahgholian, and Georg S. Weiss. Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type. AIMS Mathematics in Engineering, Special issue dedicated to Sandro Salsa on the occasion of his 70th Birthday, 2, 2020. [ DOI ]
    50 Simon Eberle and Georg S. 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 ]
    49 Georg S. Weiss. Bernoulli type free boundary problems and water waves. Geometric Measure Theory and Free Boundary Problems, Lecture Notes in Mathematics, Springer International Publishing, 2020. [ DOI ]
    48 Morteza Fotouhi, Henrik Shahgholian, and Georg S. Weiss. A free boundary problem for an elliptic system. Journal of Differential Equations, 284, 2021. [ DOI ]
    47 Simon Eberle and Georg S. Weiss. Wellen und fronten in der mathematik. UNIKATE (Journal of the University of Duisburg-Essen), (53), 2019. [ PDF ]
    46 Mariana Smit Vega Garcia, Eugen Vărvărucă, and Georg S. Weiss. Singularities in axisymmetric free boundaries for electrohydrodynamic equations. Archive for Rational Mechanics and Analysis, 222(2), 2016. [ DOI ]
    45 John Andersson, Henrik Shahgholian, Nina N. Uraltseva, and Georg S. Weiss. Equilibrium points of a singular cooperative system with free boundary. Advances in Mathematics, 280, 2015. [ DOI ]
    44 Eugen Vărvărucă and Georg S. Weiss. Singularities of steady axisymmetric free surface flows with gravity. Communications on Pure an Applied Mathematics, 67(8), 2014. [ DOI ]
    43 John Andersson, Henrik Shahgholian, and Georg S. Weiss. The singular set of higher dimensional unstable obstacle type problems. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 24(1), 2013. [ DOI ]
    42 Peter V. Gordon and Georg S. Weiss. Convective combustion in porous media: singular limit of high activation energy. Nonlinearity, 26(1), 2013. [ DOI ]
    41 Eugen Vărvărucă and Georg S. Weiss. The Stokes conjecture for waves with vorticity.  Annales de l'Institut Henri Poincaré Analyse non linéaire, 29(6), 2012. [ DOI ]
    40 John Andersson, Henrik Shahgholian, and Georg S. Weiss. Double obstacle problems with obstacles given by non-C2 Hamilton-Jacobi equations. Archive for Rational Mechanics and Analysis, 206(3), 2012. [ DOI ]
    39 Georg S. Weiss and Guanghui Zhang. The second variation of the stream function energy of water waves with vorticity. Journal of Differential Equations, 253(9), 2012. [ DOI ]
    38 Georg S. Weiss and Guanghui Zhang. A free boundary approach to two-dimensional steady capillary gravity water waves. Archive for Rational Mechanics and Analysis, 203(3), 2012. [ DOI ]
    37 Sagun Chanillo and Georg S. Weiss. A remark on the geometry of uniformly rotating stars. Journal of Differential Equations, 253(2), 2012. [ DOI ]
    36 John Andersson, Henrik Shahgholian, and Georg S. Weiss. On the singularities of a free boundary through Fourier expansion. Inventiones mathematicae, 187(3), 2012. [ DOI ]
    35 Eugen Vărvărucă and Georg S. Weiss. A geometric approach to generalized Stokes conjectures. Acta Mathematica, 206(2), 2011. [ DOI ]
    34 Georg S. Weiss and Guanghui Zhang. Existence of a degenerate singularity in the high activation energy limit of a reaction-diffusion equation. Communications in Partial Differential Equations, 35(1), 2010. [ DOI ]
    33 John Andersson, Henrik Shahgholian, and Georg S. Weiss. Regularity below the C2 threshold for a torsion problem, based on regularity for Hamilton-Jacobi equations. Nonlinear partial differential equations and related topics. American Mathematical Society Translations, 229, 2010. [ DOI ]
    32 John Andersson, Henrik Shahgholian, and Georg S. Weiss. Uniform regularity close to cross singularities in an unstable free boundary problem. Communications in Mathematical Physics, 296(1), 2010. [ DOI ]
    31 Régis Monneau and Georg S. Weiss. Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion. Ann. Inst. H. Poincaré Anal. Non Linéaire, 26(4):1207--1222, 2009. [ DOI ]
    30 Henrik Shahgholian, Nina Uraltseva, and Georg S. Weiss. A parabolic two-phase obstacle-like equation. Advances in Mathematics, 221(3), 2009. [ DOI ]
    29 John Andersson and Georg S. Weiss. A parabolic free boundary problem with Bernoulli type condition on the free boundary. Journal für die reine und angewandte Mathematik, 627, 2009. [ DOI ]
    28 Henrik Shahgholian, Nina Uraltseva, and Georg S. Weiss. The two-phase membrane problem---regularity of the free boundaries in higher dimensions. International Mathematics Research Notices, 2007, 2007. [ DOI ]
    27 Régis Monneau and Georg S. Weiss. Self-propagating high temperature synthesis (SHS) in the high activation energy regime. Acta Math. Univ. Comenian. (N.S.), 76(1):99--109, 2007. [ PDF ]
    26 Henrik Shahgholian and Georg S. Weiss. Aleksandrov and Kelvin reflection and the regularity of free boundaries. Free boundary problems. Theory and Applications, 154, 2007. [ DOI ]
    25 Régis Monneau and Georg S. Weiss. An unstable elliptic free boundary problem arising in solid combustion. Duke Mathematical Journal, 136(2), 2007. [ DOI ]
    24 John Andersson and Georg S. Weiss. Cross-shaped and degenerate singularities in an unstable elliptic free boundary problem. Journal of Differential Equations, 228(2), 2006. [ DOI ]
    23 Henrik Shahgholian and Georg S. Weiss. The two-phase membrane problem---an intersection-comparison approach to the regularity at branch points. Advanced Mathematics, 205(2), 2006. [ DOI ]
    22 Georg S. Weiss. Regularity in free boundary problems. Selected Papers on Differential Equations and Analysis. American Mathematical Society Translations, 215, 2005. [ DOI ]
    21 Henrik Shahgholian, Nina Uraltseva, and Georg S. Weiss. Global solutions of an obstacle-problem-like equation with two phases. Monatshefte Mathematik, 142(1-2), 2004. [ DOI ]
    20 Georg S. Weiss. A parabolic free boundary problem with double pinning. Nonlinear Analysis, 57(2), 2004. [ DOI ]
    19 Georg S. Weiss. Boundary monotonicity formulae and applications to free boundary problems. I. The elliptic case. Electronic Journal of Differential Equations, 44, 2004. [ PDF ]
    18 Georg S. Weiss. A singular limit arising in combustion theory: fine properties of the free boundary. Calculus of Variations and Partial Differential Equations, 17(3), 2003. [ DOI ]
    17 Hi Jun Choe and Georg S. Weiss. A semilinear parabolic equation with free boundary.  Indiana University Mathematical Journal, 52(1), 2003. [ DOI ]
    16 Georg S. Weiss. Regularity in free boundary problems. Sugaku, 54(3), 2002. (Japanese) [ PDF ]
    15 Georg S. Weiss. A gradient flow approach to a free boundary problem with volume constraint. Numerical solution of partial differential equations and related topics, 1198, 2001. [ PDF ]
    14 Georg S. Weiss. An obstacle-problem-like equation with two phases: pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary. Interfaces Free Bound, 3(2), 2001. [ DOI ]
    13 Georg S. Weiss. A singular limit arising in combustion theory: identification of the limit. Nonlinear diffusive systems--dynamics and asymptotic analysis, 1178, 2000. [ PDF ]
    12 Georg S. Weiss. The free boundary of a thermal wave in a strongly absorbing medium. Journal of Differential Equations, 160(2), 2000. [ DOI ]
    11 Georg S. Weiss. Partial regularity for a minimum problem with free boundary. The Journal Geometric Analysis, 9(2), 1999. [ DOI ]
    10 Georg S. Weiss. On the two-phase obstacle problem. Variational problems and related topics, 1117, 1999. [ PDF ]
    9 Georg S. Weiss. A homogeneity improvement approach to the heat equation with strong absorption. Variational problems and related topics, 1076, 1999. [ PDF ]
    8 Georg S. Weiss. A homogeneity improvement approach to the obstacle problem. Inventiones mathematicae, 138(1), 1999. [ DOI ]
    7 Georg S. Weiss. Self-similar blow-up and Hausdorff dimension estimates for a class of parabolic free boundary problems. SIAM Journal on Mathematical Analysis, 30(3), 1999. [ DOI ]
    6 Georg S. Weiss. Partial regularity for weak solutions of an elliptic free boundary problem. The Journal Geometric Analysis, 9(2), 1999. [ DOI ]
    5 Georg S. Weiss. Structural properties of a semilinear parabolic equation with free boundary---regularity of singular lines. Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems, Tohoku Mathematical Publications, 8, pp.189-197, 1998.
    4 Georg S. Weiss. Partial regularity for electrochemical machining with threshold current. Nonlinear evolution equations and their applications, 966, 1996. [ PDF ]
    3 Georg S. Weiss and Yasumasa Nishiura. The singular limit of the Cahn-Hilliard equation with a nonlocal term. Variational problems and related topics, 951, 1996. [ PDF ]
    2 Georg S. Weiss. Shape optimization with respect to the boundary condition of elliptic-parabolic systems. Advances in Applied Mathematics, 5(2), 1995, pp. 717–741.
    1 Georg S. Weiss. A free boundary problem for non-radial-symmetric quasi-linear elliptic equations. Advances in Applied Mathematics, 5(2), 1995, pp. 497–555.