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Dive into the research topics where Jens Habermann is active.

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Featured researches published by Jens Habermann.


Advances in Calculus of Variations | 2012

Stationary electro-rheological fluids: Low order regularity for systems with discontinuous coefficients

Verena Bögelein; Frank Duzaar; Jens Habermann; Christoph Scheven

Abstract. We establish partial regularity for solutions to systems modeling electro-rheological fluids in the stationary case. As a model case our result covers the low order regularity of systems of the type where denotes the symmetric part of the gradient , denotes the pressure, the not necessarily continuous coefficient is a bounded non-negative -function and the variable exponent function fulfills the logarithmic continuity assumption, i.e., we assume that for the modulus of continuity of the exponent function there holds To be more precise, we prove Hölder continuity of the solution outside of a negligible set. Moreover, we show that and the pressure belong to certain Morrey spaces on the regular set of , i.e., the set where is Hölder continuous. Note that under such weak assumptions partial Hölder continuity for the gradient cannot be expected. Our result is even new if the coefficient is continuous.


Advances in Calculus of Variations | 2017

Global higher integrability for non-quadratic parabolic quasi-minimizers on metric measure spaces

Yohei Fujishima; Jens Habermann

Abstract We prove up-to-the-boundary higher integrability estimates for parabolic quasi-minimizers on a domain Ω T \Omega_{T} = = Ω × \times (0,T), where Ω denotes an open domain in a doubling metric measure space which supports a Poincaré inequality. The higher integrability for upper gradients is shown globally and under optimal conditions on the boundary ∂ \partial Ω of the domain as well as on the boundary data itself. This is a starting point for a further discussion on parabolic quasi-minima on metric measure spaces, such as for example regularity or stability issues.


Journal of Mathematical Analysis and Applications | 2010

Calderón–Zygmund type estimates for a class of obstacle problems with p(x) growth

Michela Eleuteri; Jens Habermann


Mathematische Nachrichten | 2011

A Hölder continuity result for a class of obstacle problems under non standard growth conditions

Michela Eleuteri; Jens Habermann


Journal of Mathematical Analysis and Applications | 2008

Regularity results for a class of obstacle problems under nonstandard growth conditions

Michela Eleuteri; Jens Habermann


Proceedings of the London Mathematical Society | 2011

Partial Hölder continuity for discontinuous elliptic problems with VMO-coefficients

Verena Bögelein; Frank Duzaar; Jens Habermann; Christoph Scheven


Journal of Differential Equations | 2012

Calderón–Zygmund estimates for parabolic measure data equations

Paolo Baroni; Jens Habermann


Annales Academiae Scientiarum Fennicae. Mathematica | 2010

GRADIENT ESTIMATES VIA NON STANDARD POTENTIALS AND CONTINUITY

Verena Bögelein; Jens Habermann


Annales Academiae Scientiarum Fennicae. Mathematica | 2014

ELLIPTIC INTERPOLATION ESTIMATES FOR NON-STANDARD GROWTH OPERATORS

Paolo Baroni; Jens Habermann


Potential Analysis | 2014

Stability for Parabolic Quasiminimizers

Yohei Fujishima; Jens Habermann; Juha Kinnunen; Mathias Masson

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Frank Duzaar

University of Erlangen-Nuremberg

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Verena Bögelein

University of Erlangen-Nuremberg

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Christoph Scheven

University of Erlangen-Nuremberg

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