Prof. Dr. (em.) Jens Frehse

E-Mail: erdbeere(at)
Telefon: +49 228 73 3133
Raum: 4.04
Standort: Mathematics Center
Institute: Institute for Applied Mathematics
Forschungsbereiche: Research Area B
Research Area A (until 10/2012)
Research Area I (until 10/2012)
Geburtsdatum: 28.Oct 1943
Mathscinet-Number: 69105

Academic Career

1966 - 1969

Assistant Professor, University of Frankfurt

1969 - 1970

Postdoc, National Research Council (CNR), Rome, Italy


Habilitation, University of Frankfurt


DFG research, Pisa, Italy

1972 - 1973

Substitution Professor (C4), University of Heidelberg


Visiting Associate Professor, University of California, Berkeley, CA, USA

1973 - 2010

Professor (C4), University of Bonn

Since 2010

Professor Emeritus, University of Bonn

Research Profile

Mainly I consider myself as a specialist in regularity theory in the field of nonlinear elliptic and parabolic equations and variational inequalities. Besides the classical meaning, “regularity” may also mean “improved p-integrability” or “improved fractional differentiability” in situations where more regularity cannot be obtained (e.g. see my work on compressible fluids and elastic-plastic deformation with hardening). The equations considered come from continuum mechanics, fluid mechanics, Bellmann system to stochastic games. Euler equations to variational problems motivated by differential geometry. In the last two years, I developed, in collaboration with Miroslav Bulicek, several new weighted norm techniques which allow to treat a considerable broader class of variational problems with p-growth, and also stochastic differential games like Stackelberg games rather than Nash games. These techniques will be applied in the framework of mean field games in the sense of Lasry-Lions, furthermore for proving the long time existence of certain variational flows. A recent manuscript on the Prandtl Reuss problem (submitted) yields a new technique to obtain fractional derivatives of stress velocities. This improves the regularity theory of related problems in several directions.

Research Projects and Activities

DFG Collaborative Research Center SFB 611 “Singular Phenomena and Scaling in Mathematical Models”
Project leader (with S. Conti), “Analysis von Multikomponentensystemen”

DAAD Project “Stochastic Differential Games and Partial Differential Systems in Financial Markets”, Exchange program Hong Kong/Bonn

“Regularity theory for nonlinear elliptic and parabolic differential equations”

“Stationary compressible fluids”

“Long time behaviour of p-fluids”

“Regularity analysis for elastic perfect plastic deformations”

Contribution to Research Areas

Research Area A (until 10/2012)
Regularity analysis for elliptic and parabolic systems:
In [1] and [2], we constructed an irregular complex valued solution of an elliptic or parabolic scalar equation on a domain with dimension 2. This shows that the DeGiorgi-Nash theorem does not hold in the complex case. It gives a simple counter example of a real valued system with two equations.

Regularity to solutions of Euler systems to variational problems with p-growth (with Bulicek):
In [3], we obtained everywhere-Hoelder-continuity for solutions of Euler systems which are, concerning their structure, far away from Uhlenbeck-type systems. The c^<br>alpha estimate even works for a class of nonconvex coercive systems.
Research Area B
Stationary compressible fluids (with Steinhauer and Weigant):
We focused on the Navier-Stokes-equations with pressure dependent density p(<br>rho)=<br>rho^<br>gamma. We succeeded to treat physical relevant pressure laws with <br>gamma <br>geq 1. See [4], [5], [6].

p-Fluids (with Ruzicka and Malek):
In [7], we obtained long time solutions (overcoming a certain monotonicity problem). Further results (together with Ruzicka and Malek) cover the temperature dependent case.

Regularity for elastic-perfect-plastic deformations (with Loebach):
In [8], we obtained fractional boundary differentiability for the stresses which lead to a differentiability order greater 1/2. Further boundary differentiability results were obtained with Bulicek and Malek.
Research Area I (until 10/2012)
We consider Bellmann systems to stochastic differential games with Hamiltonians growing quadratically. The analytical difficulty consists in this behaviour of the Hamiltonian which leads to the problem that a lot of game problems have not been solved yet due to the unorthodox structure of the Hamiltonian. The group (Bensoussan, Bulicek, Frehse, Vogelgesang) developed new analytical tools which allowed the solution of Stackelberg games and cyclic Nash games, see [9] and “Nash and Stackelberg Differential Games”, Chinese Annales of Mathematics Series B (accepted). Furthermore we mention our work on stochastic differential games with discount control which lead to interesting new PDE aspects.

Selected Publications

[1] Jens Frehse
An irregular complex valued solution to a scalar uniformly elliptic equation
Calc. Var. Partial Differential Equations , 33: (3): 263--266
DOI: 10.1007/s00526-007-0131-8
[2] Jens Frehse, Joanna Meinel
An irregular complex-valued solution to a scalar linear parabolic equation
Int. Math. Res. Not. IMRN : Art. ID rnn 074, 7
DOI: 10.1093/imrn/rnn074
[3] Miroslav Bul\'\i \v cek, Jens Frehse
C^α-regularity for a class of non-diagonal elliptic systems with p-growth
Calc. Var. Partial Differential Equations
, 43: (3-4): 441--462
DOI: 10.1007/s00526-011-0417-8
[4] J. Frehse, M. Steinhauer, W. Weigant
The Dirichlet problem for viscous compressible isothermal Navier-Stokes equations in two dimensions
Arch. Ration. Mech. Anal. , 198: (1): 1--12
DOI: 10.1007/s00205-010-0338-2
[5] J. Frehse, M. Steinhauer, W. Weigant
The Dirichlet problem for steady viscous compressible flow in three dimensions
J. Math. Pures Appl. (9) , 97: (2): 85--97
DOI: 10.1016/j.matpur.2009.06.005
[6] J. Frehse, M. Steinhauer, W. Weigant
On stationary solutions for 2-D viscous compressible isothermal Navier-Stokes equations
J. Math. Fluid Mech. , 13: (1): 55--63
DOI: 10.1007/s00021-009-0005-2
[7] Jens Frehse, Michael R\ocirc u\v zi\v cka
Non-homogeneous generalized Newtonian fluids
Math. Z. , 260: (2): 355--375
DOI: 10.1007/s00209-007-0278-1
[8] Jens Frehse, Dominique Löbach
Regularity results for three-dimensional isotropic and kinematic hardening including boundary differentiability
Math. Models Methods Appl. Sci. , 19: (12): 2231--2262
DOI: 10.1142/S0218202509004108
[9] Miroslav Bul\'\i \v cek, Jens Frehse
On nonlinear elliptic Bellman systems for a class of stochastic differential games in arbitrary dimension
Math. Models Methods Appl. Sci. , 21: (1): 215--240
DOI: 10.1142/S0218202511005027

Publication List


• Asymptotic Analysis
• Zeitschrift Angewandte Analysis
• Differential Equations and Nonlinear Mechanics



French-German Humboldt Award

Selected Invited Lectures


Paseky, Czech Republic

2004 - 2010

Prague, Czech Republic



Offer of a Chair in Mathematics, FU Berlin


No habilitations in the last period.

Over 10 during my work at the university.

Selected PhD students

Liubov Khasina (2008): “Mathematische Behandlung von Mischungen elastoplastischer Substanzen”

Igor Huft (2008): “Einbettungen von logarithmischen Morrey-Räumen”

Dominique Löbach (2010): “Regularity analysis for problems of elastoplasticity with hardening”

Thomas Buch
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