

1966  1969  Assistant Professor, University of Frankfurt  1969  1970  Postdoc, National Research Council (CNR), Rome, Italy  1970  Habilitation, University of Frankfurt  1972  DFG research, Pisa, Italy  1972  1973  Substitution Professor (C4), University of Heidelberg  1973  Visiting Associate Professor, University of California, Berkeley, CA, USA  1973  2010  Professor (C4), University of Bonn  Since 2010  Professor Emeritus, University of Bonn 


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 pintegrability” or “improved fractional differentiability” in situations where more regularity cannot be obtained (e.g. see my work on compressible fluids and elasticplastic 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 pgrowth, 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 LasryLions, 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.


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 pfluids”
“Regularity analysis for elastic perfect plastic deformations”


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 DeGiorgiNash 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 pgrowth (with Bulicek):
In [3], we obtained everywhereHoeldercontinuity for solutions of Euler systems which are, concerning their structure, far away from Uhlenbecktype systems. The estimate even works for a class of nonconvex coercive systems.  Research Area B Stationary compressible fluids (with Steinhauer and Weigant):
We focused on the NavierStokesequations with pressure dependent density . We succeeded to treat physical relevant pressure laws with . See [4], [5], [6].
pFluids (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 elasticperfectplastic 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. 


[ 1] Jens Frehse
An irregular complex valued solution to a scalar uniformly elliptic equation Calc. Var. Partial Differential Equations , 33: (3): 263266 2008 ISSN: 09442669 DOI: 10.1007/s0052600701318[ 2] Jens Frehse, Joanna Meinel
An irregular complexvalued solution to a scalar linear parabolic equation Int. Math. Res. Not. IMRN : Art. ID rnn 074, 7 2008 ISSN: 10737928 DOI: 10.1093/imrn/rnn074[3] Miroslav Bulícek, Jens Frehse
C^αregularity for a class of nondiagonal elliptic systems with pgrowth Calc. Var. Partial Differential Equations , 43: (34): 441462 2012 ISSN: 09442669 DOI: 10.1007/s0052601104178 [ 4] J. Frehse, M. Steinhauer, W. Weigant
The Dirichlet problem for viscous compressible isothermal NavierStokes equations in two dimensions Arch. Ration. Mech. Anal. , 198: (1): 112 2010 ISSN: 00039527 DOI: 10.1007/s0020501003382[ 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): 8597 2012 ISSN: 00217824 DOI: 10.1016/j.matpur.2009.06.005[ 6] J. Frehse, M. Steinhauer, W. Weigant
On stationary solutions for 2D viscous compressible isothermal NavierStokes equations J. Math. Fluid Mech. , 13: (1): 5563 2011 ISSN: 14226928 DOI: 10.1007/s0002100900052[ 7] Jens Frehse, Michael Růzicka
Nonhomogeneous generalized Newtonian fluids Math. Z. , 260: (2): 355375 2008 ISSN: 00255874 DOI: 10.1007/s0020900702781[ 8] Jens Frehse, Dominique Löbach
Regularity results for threedimensional isotropic and kinematic hardening including boundary differentiability Math. Models Methods Appl. Sci. , 19: (12): 22312262 2009 ISSN: 02182025 DOI: 10.1142/S0218202509004108[ 9] Miroslav Bulícek, Jens Frehse
On nonlinear elliptic Bellman systems for a class of stochastic differential games in arbitrary dimension Math. Models Methods Appl. Sci. , 21: (1): 215240 2011 ISSN: 02182025 DOI: 10.1142/S0218202511005027



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


1992  FrenchGerman Humboldt Award 


1994  Paseky, Czech Republic  2004  2010  Prague, Czech Republic 


1980  Offer of a Chair in Mathematics, FU Berlin 


No habilitations in the last period.
Over 10 during my work at the university.


Liubov Khasina (2008): “Mathematische Behandlung von Mischungen elastoplastischer Substanzen”
Igor Huft (2008): “Einbettungen von logarithmischen MorreyRäumen”
Dominique Löbach (2010): “Regularity analysis for problems of elastoplasticity with hardening”
Thomas Buch


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