Matthias Georg Hieber

教授(任期付)

  • 1807 Citations
  • 18 h-Index
1989 …2019
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Research Output 1989 2019

  • 1807 Citations
  • 18 h-Index
  • 66 Article
  • 5 Chapter
  • 3 Conference contribution
  • 2 Editorial
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Article
2019

A Characterization of Harmonic Lr -Vector Fields in Two-Dimensional Exterior Domains

Hieber, M. G., Kozono, H., Seyfert, A., Shimizu, S. & Yanagisawa, T., 2019 Jan 1, In : Journal of Geometric Analysis.

Research output: Contribution to journalArticle

Exterior Domain
Vector Field
Harmonic
Unit normal vector
Simple Closed Curve
Nematic liquid crystals
Topology
Nematic Liquid Crystal
Equilibrium Point
Global Solution

Optimal decay rates for solutions to the incompressible Oldroyd-B model in R 3

Hieber, M. G., Wen, H. & Zi, R., 2019 Jan 29, In : Nonlinearity. 32, 3, p. 833-852 20 p.

Research output: Contribution to journalArticle

Decay Estimates
Decay Rate
decay rates
Weak Solution
Large Data
2018
1 Citation (Scopus)

On the bidomain problem with FitzHugh–Nagumo transport

Hieber, M. G. & Prüss, J., 2018 Jun 14, (Accepted/In press) In : Archiv der Mathematik. p. 1-15 15 p.

Research output: Contribution to journalArticle

Evolution Equation
Semilinear Evolution Equation
Local Well-posedness
Energy Estimates
Operator

Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces

Hieber, M. G., Mahalov, A. & Takada, R., 2018 Jan 1, (Accepted/In press) In : Journal of Differential Equations.

Research output: Contribution to journalArticle

Stratified Fluid
Rotating Fluid
Time-periodic Solutions
Buoyancy
Fluids
2017
1 Citation (Scopus)

Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces

Galdi, G. P., Hieber, M. G. & Kashiwabara, T., 2017 Sep 18, In : Nonlinearity. 30, 10, p. 3979-3992 14 p.

Research output: Contribution to journalArticle

primitive equations
Primitive Equations
Time-periodic Solutions
periodic functions
time functions
2016
14 Citations (Scopus)

A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems

Geissert, M., Hieber, M. G. & Nguyen, T. H., 2016 Jun 1, In : Archive for Rational Mechanics and Analysis. 220, 3, p. 1095-1118 24 p.

Research output: Contribution to journalArticle

Viscous Flow
Incompressible Flow
Viscous Fluid
Incompressible Fluid
Fluid Flow
16 Citations (Scopus)

Dynamics of nematic liquid crystal flows: The quasilinear approach

Hieber, M. G., Nesensohn, M., Pruss, J. & Schade, K., 2016 Mar 1, In : Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis. 33, 2, p. 397-408 12 p.

Research output: Contribution to journalArticle

Nematic liquid crystals
Nematic Liquid Crystal
Strong Solution
Dynamics (theory)
Parabolic Equation
4 Citations (Scopus)

Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic case

Hieber, M. G. & Prüss, J., 2016 Aug 2, (Accepted/In press) In : Mathematische Annalen. p. 1-20 20 p.

Research output: Contribution to journalArticle

Topology
Local Solution
Stress Tensor
Nematic Liquid Crystal
Strong Solution
3 Citations (Scopus)

Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion

Hieber, M., Hussein, A. & Kashiwabara, T., 2016 Dec 15, In : Journal of Differential Equations. 261, 12, p. 6950-6981 32 p.

Research output: Contribution to journalArticle

Primitive Equations
Salinity
Well-posedness
Interpolation
Heat
9 Citations (Scopus)

Global Strong Well-Posedness of the Three Dimensional Primitive Equations in Lp -Spaces

Hieber, M. G. & Kashiwabara, T., 2016 Sep 1, In : Archive for Rational Mechanics and Analysis. 221, 3, p. 1077-1115 39 p.

Research output: Contribution to journalArticle

Primitive Equations
Lp Spaces
Well-posedness
Hydrostatics
Strong Solution

Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids

Hieber, M. G. & Saito, H., 2016 Sep 19, (Accepted/In press) In : Journal of Evolution Equations. p. 1-24 24 p.

Research output: Contribution to journalArticle

Non-Newtonian Fluid
Free Boundary Problem
Strong Solution
Stress Tensor
Class
2015
5 Citations (Scopus)

Pointwise upper bounds for the solution of the Stokes equation on Lσ∞(Ω) and applications

Bolkart, M. & Hieber, M. G., 2015 Apr 1, In : Journal of Functional Analysis. 268, 7, p. 1678-1710 33 p.

Research output: Contribution to journalArticle

Stokes Equations
Semigroup
Upper bound
Stokes
Denote
14 Citations (Scopus)

Stokes resolvent estimates in spaces of bounded functions

Abe, K., Giga, Y. & Hieber, M. G., 2015 May 1, In : Annales Scientifiques de l'Ecole Normale Superieure. 48, 3, p. 537-559 23 p.

Research output: Contribution to journalArticle

Resolvent Estimates
Stokes
Analytic Semigroup
Stokes Operator
Stokes Equations
3 Citations (Scopus)

The Lp-approach to the fluid-rigid body interaction problem for compressible fluids

Hieber, M. G. & Murata, M., 2015, In : Evolution Equations and Control Theory. 4, 1, p. 69-87 19 p.

Research output: Contribution to journalArticle

Compressible Fluid
Strong Solution
Rigid Body
System of equations
Fluid
2014
1 Citation (Scopus)
Exterior Domain
Strong Solution
Global Existence
Velocity Field
Navier Stokes equations
1 Citation (Scopus)

Stability results for fluids of Oldroyd-B type on exterior domains

Geissert, M., Hieber, M. G. & Huy, N. T., 2014 Sep 24, In : Journal of Mathematical Physics. 55, 9, 091505.

Research output: Contribution to journalArticle

Exterior Domain
Fluid
Analytic Semigroup
fluids
2013
20 Citations (Scopus)

Global existence results for Oldroyd-B fluids in exterior domains: The case of non-small coupling parameters

Fang, D., Hieber, M. G. & Zi, R., 2013 Oct, In : Mathematische Annalen. 357, 2, p. 687-709 23 p.

Research output: Contribution to journalArticle

Oldroyd-B Fluid
Exterior Domain
Global Existence
Existence Results
Global Solution
11 Citations (Scopus)

Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids

Geissert, M., Götze, K. & Hieber, M. G., 2013, In : Transactions of the American Mathematical Society. 365, 3, p. 1393-1439 47 p.

Research output: Contribution to journalArticle

Newtonian Fluid
Strong Solution
Rigid Body
Exponent
Fluid

Remarks on the theory of Oldroyd-B fluids in exterior domains

Hieber, M. G., 2013 Oct, In : Discrete and Continuous Dynamical Systems - Series S. 6, 5, p. 1307-1313 7 p.

Research output: Contribution to journalArticle

Oldroyd-B Fluid
Exterior Domain
Boundary conditions
Fluids
Global Existence
2 Citations (Scopus)

Stochastic stability of the Ekman spiral

Hieber, M. G. & Stannat, W., 2013, In : Annali della Scuola Normale - Classe di Scienze. 12, 1, p. 189-208 20 p.

Research output: Contribution to journalArticle

Stochastic Stability
Navier-Stokes
Martingale
Boundary conditions
Stationary Solutions

Well-posedness results for the navier-stokes equations in the rotational framework

Hieber, M. G. & Monniaux, S., 2013 Nov, In : Discrete and Continuous Dynamical Systems- Series A. 33, 11-12, p. 5143-5151 9 p.

Research output: Contribution to journalArticle

Ill-posedness
Open set
Well-posedness
Dirichlet Boundary Conditions
Navier Stokes equations
2012
3 Citations (Scopus)

Density-dependent incompressible viscous fluid flow subject to linearly growing initial data

Fang, D., Hieber, M. G. & Zhang, T., 2012 Aug, In : Applicable Analysis. 91, 8, p. 1477-1493 17 p.

Research output: Contribution to journalArticle

Viscous Flow
Viscous Fluid
Incompressible Fluid
Navier Stokes equations
Fluid Flow
23 Citations (Scopus)

Global existence results for Oldroyd-B fluids in exterior domains

Hieber, M. G., Naito, Y. & Shibata, Y., 2012 Feb 1, In : Journal of Differential Equations. 252, 3, p. 2617-2629 13 p.

Research output: Contribution to journalArticle

Oldroyd-B Fluid
Exterior Domain
Global Existence
Existence Results
Fluids
20 Citations (Scopus)

Weak Neumann implies Stokes

Geissert, M., Heck, H., Hieber, M. G. & Sawada, O., 2012 Aug, In : Journal fur die Reine und Angewandte Mathematik. 669, p. 75-100 26 p.

Research output: Contribution to journalArticle

Hermann Von Helmholtz
Stokes
Projection
Imply
2011
7 Citations (Scopus)

The spin-coating process: Analysis of the free boundary value problem

Denk, R., Geissert, M., Hieber, M. G., Saal, J. & Sawada, O., 2011 Jul, In : Communications in Partial Differential Equations. 36, 7, p. 1145-1192 48 p.

Research output: Contribution to journalArticle

Free Boundary Value Problems
Spin coating
Boundary value problems
Coating
Regularity
2010
5 Citations (Scopus)

L -estimates for parabolic systems with VMO-coefficients

Heck, H., Hieber, M. G. & Stavrakidis, K., 2010 Jun, In : Discrete and Continuous Dynamical Systems - Series S. 3, 2, p. 299-309 11 p.

Research output: Contribution to journalArticle

Parabolic Systems
Coefficient
A Priori Estimates
Estimate
Parabolic Equation
18 Citations (Scopus)

Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem

Geissert, M., Hess, M., Hieber, M. G., Schwarz, C. & Stavrakidis, K., 2010 Mar, In : Journal of Mathematical Fluid Mechanics. 12, 1, p. 47-60 14 p.

Research output: Contribution to journalArticle

Sectorial Operator
Stokes Operator
Exterior Domain
Stokes Equations
Bounded Domain
9 Citations (Scopus)

Nonlinear stability of Ekman boundary layers

Hess, M., Hieber, M. G., Mahalov, A. & Saal, J., 2010 Aug, In : Bulletin of the London Mathematical Society. 42, 4, p. 691-706 16 p.

Research output: Contribution to journalArticle

Nonlinear Stability
Boundary Layer
Stationary Solutions
Decay Rate
Half-space
2 Citations (Scopus)

Remarks on the L p-approach to the stokes equation on unbounded domains

Geissert, M., Heck, H., Hieber, M. G. & Sawada, O., 2010 Jun, In : Discrete and Continuous Dynamical Systems - Series S. 3, 2, p. 291-297 7 p.

Research output: Contribution to journalArticle

Stokes Operator
Analytic Semigroup
Stokes Equations
Hermann Von Helmholtz
Unbounded Domain
38 Citations (Scopus)

The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework

Hieber, M. G. & Shibata, Y., 2010 Jun, In : Mathematische Zeitschrift. 265, 2, p. 481-491 11 p.

Research output: Contribution to journalArticle

Mild Solution
Navier-Stokes Equations
Norm
Arbitrary
Framework
2009
12 Citations (Scopus)

Global properties of generalized Ornstein-Uhlenbeck operators on Lp (RN, RN) with more than linearly growing coefficients

Hieber, M. G., Lorenzi, L., Prüss, J., Rhandi, A. & Schnaubelt, R., 2009 Feb 1, In : Journal of Mathematical Analysis and Applications. 350, 1, p. 100-121 22 p.

Research output: Contribution to journalArticle

Ornstein-Uhlenbeck Operator
Lp Estimates
Gradient Estimate
Strongly Continuous Semigroups
Pointwise Estimates
8 Citations (Scopus)
Stokes Flow
Strong Solution
Navier-Stokes
Mild Solution
Rotating
2008
3 Citations (Scopus)

Irreducibility and mixed boundary conditions

Haller-Dintelmann, R., Hieber, M. G. & Rehberg, J., 2008 Feb, In : Positivity. 12, 1, p. 83-91 9 p.

Research output: Contribution to journalArticle

Positive Semigroup
Nonsmooth Domains
Mixed Boundary Conditions
Irreducibility
Neumann Boundary Conditions
24 Citations (Scopus)

Quasilinear parabolic systems with mixed boundary conditions on nonsmooth domains

Hieber, M. G. & Rehberg, J., 2008, In : SIAM Journal on Mathematical Analysis. 40, 1, p. 292-305 14 p.

Research output: Contribution to journalArticle

Quasilinear Parabolic Systems
Nonsmooth Domains
Maximal Regularity
Kernel Estimate
Quasilinear System
2007
1 Citation (Scopus)

Lp-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Geissert, M. & Hieber, M. G., 2007, In : Acta Mathematica Universitatis Comenianae. 76, 1, p. 69-76 8 p.

Research output: Contribution to journalArticle

Stokes Flow
Navier-Stokes
Rotating
115 Citations (Scopus)

Optimal L p -L q -estimates for parabolic boundary value problems with inhomogeneous data

Denk, R., Hieber, M. G. & Prüss, J., 2007 Sep, In : Mathematische Zeitschrift. 257, 1, p. 193-224 32 p.

Research output: Contribution to journalArticle

Boundary Value Problem
Triebel-Lizorkin Space
General Boundary Conditions
Ellipticity
Parabolic Problems
2006
25 Citations (Scopus)

Lp - Lq Estimates for parabolic systems in non-divergence form with VMO coefficients

Haller-Dintelmann, R., Heck, H. & Hieber, M. G., 2006 Dec, In : Journal of the London Mathematical Society. 74, 3, p. 717-736 20 p.

Research output: Contribution to journalArticle

Lp Estimates
Parabolic Systems
Muckenhoupt Weights
Coefficient
Unique Solution
61 Citations (Scopus)

L p-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle

Geissert, M., Heck, H. & Hieber, M. G., 2006 Jul 1, In : Journal fur die Reine und Angewandte Mathematik. 596, p. 45-62 18 p.

Research output: Contribution to journalArticle

Stokes Flow
Navier-Stokes
Rotating
Navier-Stokes Problem
Stokes Equations
2005
3 Citations (Scopus)

H ∞-calculus for products of non-commuting operators

Haller-Dintelmann, R. & Hieber, M. G., 2005 Sep, In : Mathematische Zeitschrift. 251, 1, p. 85-100 16 p.

Research output: Contribution to journalArticle

Commutator Estimate
Sectorial Operator
Calculus
Banach space
Operator
41 Citations (Scopus)

The Navier-Stokes equations in ℝn with linearly growing initial data

Hieber, M. G. & Sawada, O., 2005 Feb, In : Archive for Rational Mechanics and Analysis. 175, 2, p. 269-285 17 p.

Research output: Contribution to journalArticle

Navier-Stokes
Navier Stokes equations
Navier-Stokes Equations
Semigroup
Linearly
2003
16 Citations (Scopus)

Maximal Lp-regularity for elliptic operators with VMO-coefficients

Heck, H. & Hieber, M. G., 2003, In : Journal of Evolution Equations. 3, 2, p. 332-359 28 p.

Research output: Contribution to journalArticle

Parabolic Problems
Elliptic Operator
Regularity
Coefficient
10 Citations (Scopus)

Muckenhoupt weights and maximal Lp-regularity

Haller, R., Heck, H. & Hieber, M. G., 2003 Oct, In : Archiv der Mathematik. 81, 4, p. 422-430 9 p.

Research output: Contribution to journalArticle

Muckenhoupt Weights
Weighted Estimates
Elliptic Operator
Differential operator
Regularity
411 Citations (Scopus)

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

Denk, R., Hieber, M. G. & Prüss, J., 2003 Nov, In : Memoirs of the American Mathematical Society. 788

Research output: Contribution to journalArticle

R-boundedness
Fourier multipliers
Boundary value problems
Mathematical operators
Operator-valued Fourier multipliers
2001
71 Citations (Scopus)

Lp-Theory of the Stokes equation in a half space

Desch, W., Hieber, M. G. & Prüss, J., 2001, In : Journal of Evolution Equations. 1, 1, p. 115-142 28 p.

Research output: Contribution to journalArticle

Stokes Equations
half space
Half-space
Resolvent Equations
Stokes Operator
2000
8 Citations (Scopus)

Heat-kernels and maximal Lp - Lq estimates: The non-autonomous case

Hieber, M. G. & Monniaux, S., 2000, In : Journal of Fourier Analysis and Applications. 6, 5, p. 467-481 15 p.

Research output: Contribution to journalArticle

Lp Estimates
Heat Kernel
Semilinear
Parabolic Equation
Semigroup
6 Citations (Scopus)

Heat-Kernels and Maximal LP-Lq-Estimates: The Non-Autonomous Case

Hieber, M. G. & Monniaux, S., 2000, In : Journal of Knot Theory and its Ramifications. 6, 5, p. 467-481 15 p.

Research output: Contribution to journalArticle

Lp Estimates
Nonautonomous Equation
Heat Kernel
Semilinear
Parabolic Equation
19 Citations (Scopus)
Maximal Regularity
Nonautonomous Equation
Pseudodifferential Operators
Parabolic Equation
Regularity
1999
8 Citations (Scopus)

Lp spectral independence of elliptic operators via commutator estimates

Hieber, M. G. & Schrohe, E., 1999, In : Positivity. 3, 3, p. 259-272 14 p.

Research output: Contribution to journalArticle

Commutator Estimate
Electric commutators
Elliptic Operator
C0-semigroup
Coefficient

Noyaux de la chaleur et estimations mixtes Lp - Lq optimales: Le cas non autonome

Translated title of the contribution: Heat kernel and maximal Lp - Lq estimates: The non-autonomous caseHieber, M. G. & Monniaux, S., 1999 Feb, In : Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 328, 3, p. 233-238 6 p.

Research output: Contribution to journalArticle

Lp Estimates
Analytic Semigroup
Heat Kernel
A Priori Estimates
Commutator