Prof. Dr. Matthias Hieber
Applied Analysis

Prof. Dr. Matthias Hieber

Contact

work +49 6151 16-21475
fax +49 6151 16-21483

Work S2|15 419
Schlossgartenstraße 7
64289 Darmstadt

Research Interests

  • Partial Differential Equations
  • Fluid Dynamics
  • Evolution Equations
  • Harmonic Analysis
  • M. Hieber, A. Hussein, M. Wrona, Strong well-posedness of the Q-tensor model for liquid crystals: the case of arbitrary ratio of tumbling and alignments effects. Arch. Rational Mech. Anal, to appear
  • R. Danchin, M. Hieber, P. Mucha, P. Tolksdorf, Free boundary problems by Da Prato-Grisvard theory. Memoirs Amer. Math. Soc, to appear
  • T. Binz, M. Hieber, A. Hussein, M. Saal, The primitive equations with stochastic wind driven boundary conditions. J. Math. Pures Appl. 183, (2021), 76-101
  • M. Hieber, H. Kozono, A. Seyfert, S. Shimizu, T. Yanagisawa, $L^r$-Helmholtz-Weyl decomposition for three dimensional exterior domains. J. Funct. Anal., 281, (2021), 109144.
  • M. Hieber, J. Prüss, Bounded $H^\infty$-calculus for a class of nonlocal operators: the bidomain operator in the $L_q$-setting. Math. Ann., 378, (2020), 6502-6516.
  • Y. Giga, M. Gries, M. Hieber, A. Hussein, T. Kashiwabara, The hydrostatic Stokes operator and well-posedness of the primitive equations on spaces of bounded functions. J. Funct. Anal., 279 (2020), 108561.
  • M. Hieber, J. Prüss, Dynamics of Ericksen-Leslie equations with general Leslie stress II: The compressible isotropic case. Arch. Rational Mech. Anal., {233}, (2019), 1441-1468.
  • M. Hieber, J. Prüss, Modeling and analysis of Ericksen-Leslie equations for nematic liquid crystal flow. In: Handbook of Math. Anal. in Mechanics of Viscous Fluids, Y. Giga, A. Novotny (eds.), Vol.2, Springer, 2018, 1057-1134.
  • M. Hieber, J. Saal, The Stokes equation in the $L^p$-setting: well-posedness and regularity properties. In: Handbook of Math. Anal. in Mechanics of Viscous Fluids, Y. Giga, A. Novotny (eds.), Vol.1, Springer, 2018, 117-206.
  • Matthias Hieber, Jan Prüss, Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic case. Math. Annalen, 369 (3-4), (2017), 977-996.
  • M. Hieber, T. Kashiwabara, Strong well-posedness of the three dimensional primitive equations in the $L^p$-setting. Arch. Ration. Mech. Anal., {221} (2016), 1077--1115.
  • M. Geissert, M. Hieber, H. Nguyen, A general approach to time periodic incompressible viscous fluid flow problems. Arch. Rational Mech. Anal., {220} (2016), 1095-1118.
  • K. Abe, M. Hieber, Y. Giga, Stokes resolvent estimates in spaces of bounded functions. Ann. Sci. Ec. Norm. Super., {48}, (2015), 521-543.
  • D. Fang, M. Hieber, R. Zi, Global existence results for Oldroyd-B fluids on exterior domains with non small coupling parameters. Math. Ann., {356} (2013), 687-709.
  • M. Geissert, M. Hieber, H. Heck, O. Sawada, Weak Neumann implies Stokes. J. reine angew. Math., {669}, (2012), 75-100.
  • R. Denk, M. Hieber, J. Prüss, Optimal $L^p-L^q$ estimates for parabolic boundary value problems with inhomogeneous boundary data}. Math. Z., 257, (2007), 193-224.
  • M. Hieber, M. Geissert, H. Heck, $L^p$-theory of the Navier-Stokes flow in the exterior of a rotating or moving domain. J. reine angew. Math., 596 (2006), 45-62.
  • R. Denk, M. Hieber, G. Dore, J. Prüss, A. Venni, New thoughts on old ideas of R.T. Seeley. Math. Ann., 328 (2004), 545-583.
  • R. Denk, M. Hieber, J. Prüss, R-boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type, Memoirs Amer. Math. Soc., vii + 114pp., 2003.
  • M. Hieber, J. Prüss, Heat kernels and maximal $L^p$-$L^q$-estimates for solutions of parabolic evolution equations. Comm. Partial Differential Equations, 22 (1997), 1647-1669.

Matthias Hieber, James Robinson, Yoshihito Shibata

Mathematical Analysis of the Navier-Stokes Equations

Lecture Notes in Mathematics 2254, Springer, 2020

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Matthias Hieber

Analysis I

Springer, 2018

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Matthias Hieber

Analysis II

Springer, 2019

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Robert Denk, Matthias Hieber, Jan Prüss

R-Boundeness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

Memoirs of the American Mathematical Society, 2003

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Wolfgang Arendt, Charles Batty, Matthias Hieber, Frank Neubrander

Vector-Valued Laplace Transforms and Cauchy Problems

Birkhäuser Monographs in Mathematics, 2001 and 2011

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