Publications of Hans-Christoph Grunau

Monograph

Gazzola, F.; Grunau, H.-Ch.; Sweers, G.:

Polyharmonic boundary value problems,
Positivity preserving and nonlinear higher order elliptic equations in bounded domains.
Springer Lecture Notes in Mathematics 1991, Springer-Verlag: Heidelberg etc., 2010.
[Pdf]
[Errata] (as uncovered so far)
Copyright: Springer-Verlag. The original monograph is available on http://link.springer.com/

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Lecture notes

Grunau, H.-Ch.:

Abbildungsgrad und Fixpunktsätze (Degree of mapping and fixed point theorems),
Vorlesungsausarbeitung, basiert auf Vorlesungen von E. Heinz (Göttingen)
Lecture notes, based upon lectures of E. Heinz (Göttingen)
[Ps] [Pdf] [Dvi]

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Lehrbuch

Grauert, H., Grunau, H.-Ch.:

Lineare Algebra und analytische Geometrie,
Copyright: Oldenbourg-Verlag, 1999-2009.
Ab 2009: Alle Rechte bei den Autoren.
[PS-Datei] [DVI-Datei] [PDF-Datei]

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Habilitationsschrift (1996)
Polyharmonische Dirichletprobleme: Positivität, kritische Exponenten und
kritische Dimensionen
[Ps] [Pdf] [Dvi]
English Summary
[Ps] [ Pdf] [Dvi]

Articles

Grunau, H.-Ch.; Romani, G.:

Unexpected differences between fundamental solutions of general higher-order elliptic operators and of products of second-order operators.
[Pdf]

Grunau, H.-Ch.:

Boundary Value Problems for the Willmore Functional.
Survey article, submitted to RIMS Kokyuroku series,
Proceedings of the workshop ``Analysis of Shapes of Solutions to Partial Differential Equations'', June 27-29, 2018.
[Pdf]

Eichmann, S.; Grunau, H.-Ch.:

Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions.
Adv. Calc. Var., to appear.
[Pdf]
Copyright: de Gruyter. The original article is available on https://www.degruyter.com/view/j/acv

Dipierro, S.; Grunau, H.-Ch.:

Boggio's formula for fractional polyharmonic Dirichlet problems.
Ann. Mat. Pura Appl. (1923-) 196, 1327-1344 (2017).
[Pdf]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Deckelnick, K.; Grunau, H.-Ch.; Röger, M:

Minimising a relaxed Willmore functional for graphs subject to boundary conditions.
Interfaces Free Bound. 19, 109-140 (2017).
[Pdf]
Copyright: EMS - European Mathematical Society Publishing House.
The original article is available on https://www.ems-ph.org/journals/journal.php?jrn=ifb

Grunau, H.-Ch.; Lenor, St.:

Uniform estimates and convexity in capillary surfaces.
Nonlinear Analysis A: T.M.A. 97, 83-93 (2014).
[Pdf]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Grunau, H.-Ch.; Sweers, G.:

In any dimension a "clamped plate" with a uniform weight may change sign.
Nonlinear Analysis A: T.M.A. 97, 119-124 (2014).
[Pdf]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Grunau, H.-Ch.; Sweers, G.:

A clamped plate with a uniform weight may change sign.
Discrete Cont. Dynam. Systems - S (Proceedings etc.) 7, 761 - 766 (2014)
[Pdf]
Copyright: American Institute of Mathematical Sciences, first published with AIMS Press.

Grunau, H.-Ch.; Robert, F.:

Uniform estimates for polyharmonic Green functions in domains with small holes.
In: J. Serrin, E. Mitidieri, V. Radulescu (eds.), Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems.
Contemporary Mathematics 595, 263-272 (2013).
[Ps] [Pdf] [Dvi]
Copyright: American Mathematical Society. The original article is available on http://www.ams.org/books/conm/595/

Grunau, H.-Ch.:

The asymptotic shape of a boundary layer of symmetric Willmore surfaces of revolution.
In: C. Bandle et al. (eds.), Inequalities and Applications 2010.
International Series of Numerical Mathematics 161, 19-29 (2012).
[Ps] [Pdf]
Copyright: Springer Basel. The original article is available on http://link.springer.com/

Grunau, H.-Ch.; Robert, F.; Sweers, G.:

Optimal estimates from below for biharmonic Green functions.
Proc. Amer. Math. Society 139, 2151-2161 (2011).
[Pdf]
Copyright: American Mathematical Society AMS. The original article is available on http://www.ams.org/journals/proc/

Gazzola, F.; Grunau, H.-Ch.; Sweers, G.:

Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions.
Ann. Mat. Pura Appl. 189, 475-486 (2010).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Dall'Acqua, A., Fröhlich, St., Grunau, H.-Ch., Schieweck, F.:

Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data.
Adv. Calc. Var. 4, 1-81 (2011).
[Ps] [Pdf]
Copyright: de Gruyter. The original article is available on https://www.degruyter.com/view/j/acv

Grunau, H.-Ch.:

Nonlinear questions in clamped plate models (Survey article).
Milan J. Math. 77, 171-204 (2009).
[Ps.gz] [Pdf]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

Deckelnick, K. , Grunau, H.-Ch.:

A Navier boundary value problem for Willmore surfaces of revolution.
Analysis 29, 229-258 (2009).
[Ps] [Pdf]
Copyright: de Gruyter. The original article is available on http://www.degruyter.com/

Gazzola, F., Grunau, H.-Ch.:

Some new properties of biharmonic heat kernels.
Nonlinear Analysis T.M.A. 70, 2965 - 2973 (2009).
[Ps] [Pdf] [Dvi]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Dall'Acqua, A., Deckelnick, K., Grunau, H.-Ch.:

Classical solutions to the Dirichlet problem for Willmore surfaces of revolution.
Adv. Calc. Var. 1, 379 - 397 (2008).
[Ps] [Pdf] [Dvi]
Copyright: de Gruyter. The original article is available on https://www.degruyter.com/view/j/acv

Ferrero, A., Grunau, H.-Ch., Karageorgis, P.:

Supercritical biharmonic equations with power-type nonlinearity.
Ann. Mat. Pura Appl. 188, 171 - 185 (2009).
[Ps] [Pdf] [Dvi], http://arxiv.org/abs/0711.2202
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Ferrero, A., Gazzola, F., Grunau, H.-Ch.:

Decay and eventual local positivity for biharmonic parabolic equations.
Discrete Cont. Dynam. Systems 21, 1129 - 1157 (2008).
[Ps] [Pdf] [Dvi]
Copyright: American Institute of Mathematical Sciences, first published with AIMS Press.

Deckelnick, K., Grunau, H.-Ch.:

Stability and symmetry in the Navier problem for the one-dimensional Willmore equation.
SIAM J. Math. Anal. 40, 2055 - 2076 (2009).
[Ps] [Pdf]
Copyright: SIAM. The original article is available on http://epubs.siam.org/SIMA/sima_toc.html

Grunau, H.-Ch., Robert, F.:

Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions.
Arch. Rational Mech. Anal., 195, 865-898 (2010).
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/
Preprint versions:
Stability of the positivity of biharmonic Green's functions under perturbations of the domain.
[Ps] [Pdf] [Dvi],
Positivity issues of biharmonic Green's functions under Dirichlet boundary conditions.
[Ps] [Pdf] [Dvi], http://arxiv.org/abs/0705.3301
Research announcement:
Boundedness of the negative part of biharmonic Green's functions under Dirichlet boundary conditions in general domains.
C. R. Math. Acad. Sci. Paris , Ser. I 347, 163 - 166 (2009).
Copyright: Academie des Sciences / Elsevier Masson SAS.
The article is available on http://www.sciencedirect.com/science/journal/1631073X.

Gazzola, F., Grunau, H.-Ch.:

Local eventual positivity for a biharmonic heat equation in R^n.
Discrete Cont. Dynam. Systems - S (Proceedings etc.) 1, 83 - 87 (2008).
[Ps] [Pdf] [Dvi]
Copyright: American Institute of Mathematical Sciences, first published with AIMS Press.

Grunau, H.-Ch., Ould Ahmedou, M., Reichel, W.:

The Paneitz equation in hyperbolic space.
Annales Inst. H. Poincare (C) Nonlinear Analysis 25, 847 - 864 (2008).
[Ps] [Pdf] [Dvi]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Ferrero, A., Grunau, H.-Ch.:

The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity.
J. Differ. Equations 234, 582 - 606 (2007).
[Ps] [Pdf] [Dvi]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Arioli, G., Gazzola, F., Grunau, H.-Ch., Sassone, E.:

The second bifurcation branch for radial solutions of the Brezis-Nirenberg problem in dimension four.
Nonl. Differ. Equ. Appl. NoDEA 15, 69-90 (2008).
[Ps] [Pdf] [Files for computer assisted proof]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

Grunau, H.-Ch., Sweers, G.:

Regions of positivity for polyharmonic Green functions in arbitrary domains.
Proc. Amer. Math. Society 135, 3537-3546 (2007).
[Ps] [Pdf] [Dvi]
Copyright: AMS. The original article is available on http://www.ams.org/journals/proc/

Berchio, E., Grunau, H.-Ch.:

Local regularity of weak solutions of semilinear parabolic systems with critical growth.
J. Evolution equations 7, 177-196 (2007).
[Ps] [Pdf] [Dvi]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

Gazzola, F., Grunau, H.-Ch.:

Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay.
Calc. Var. 30, 389-415 (2007).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Arioli, G., Gazzola, F., Grunau, H.-Ch.:

Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity.
J. Differ. Equations 230, 743 - 770 (2006).
[Ps] [Pdf] [Files for computer assisted proof]
Copyright: Elsevier. The original article is available on http://www.sciencedirect.com/

Deckelnick, K., Grunau, H.-Ch.:

Boundary value problems for the one-dimensional Willmore equation,
Calc. Var. 30, 293-314 (2007).
[Ps] [Pdf]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/
Preliminary and more special version: Technical Report 05-02, University of Magdeburg.
[Ps] [Pdf]

Gazzola, F., Grunau, H.-Ch.:

Radial entire solutions for supercritical biharmonic equations.
Math. Annal. 334, 905 - 936 (2006).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Grunau, H.-Ch., Kühnel, M.:

On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds,
Math. Z. 249, 297-327 (2005).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Arioli, G., Gazzola, F., Grunau, H.-Ch., Mitidieri, E.:

A semilinear fourth order elliptic problem with exponential nonlinearity,
SIAM J. Math. Anal. 36, 1226-1258 (2005).
[Ps] [Pdf] [Files for computer assisted proof]
Copyright: SIAM. The original article is available on http://www.siam.org/journals/sima/sima.htm

Dall'Acqua, A., Grunau, H.-Ch., Sweers, G.:

On a conditioned Brownian motion and a maximum principle on the disk,
J. Anal. 93, 309-329 (2004).
[Ps] [Pdf] [Dvi]

Gazzola, F., Grunau, H.-Ch., Squassina, M.:

Existence and nonexistence results for critical growth biharmonic elliptic equations,
Calc. Var. PDE 18, 117-143 (2003).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Gazzola, F., Grunau, H.-Ch., Mitidieri, E.:

Hardy inequalities with optimal constants and remainder terms,
Transactions Amer. Math. Soc. 356, 2149-2168 (2004).
[Ps] [Pdf] [Dvi]
Copyright: AMS. The original article is available on http://www.ams.org/tran/

Grunau, H.-Ch., Sweers, G.:

Optimal conditions for anti-maximum principles,
Ann. Sc. Norm. Sup. Pisa. Cl. Sci. (4) 30, 499-513 (2001).

Grunau, H.-Ch.:

Positivity, change of sign and buckling eigenvalues in a one-dimensional fourth order model problem,
Adv. Differ. Equations. 7, 177-196 (2002).
[Ps] [Pdf]
Copyright: Khayyam-Publishing http://projecteuclid.org/euclid.ade/

Grunau, H.-Ch., Sweers, G.:

Sharp estimates for iterated Green functions,
Proc. Royal Soc. Edinburgh. 132A, 91-120 (2002).
[Ps] [Pdf] [Dvi]
This article is reproduced by permission of the Royal Society of Edinburgh.
The original article is available on http://ninetta.ingentaselect.com/

Grunau, H.-Ch., Sweers, G.:

Nonexistence of local minima of supersolutions for the circular clamped plate,
Pacific J. Math 198, 437-442 (2001).
[Ps] [Pdf] [Dvi]
The original article is available on http://msp.org/pjm/

Gazzola, F., Grunau, H.-Ch.:

Critical dimensions and higher order Sobolev inequalities with remainder terms,
Nonl. Differ. Equ. Appl. NoDEA 8, 35-44 (2001).
[Ps] [Pdf] [Dvi]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

Gazzola, F., Grunau, H.-Ch.:

On the role of space dimension $n=2+2sqrt{2}$ in the semilinear Brezis-Nirenberg eigenvalue problem,
Analysis 20, 395-399 (2000).
[Ps] [Pdf] [Dvi]
Copyright: de Gruyter http://www.degruyter.com

Grunau, H.-Ch., Sweers, G.:

Sign change for the Green function and for the first eigenfunction of equations of clamped plate type,
Archive Rational Mech. Anal. 150, 179-190 (1999).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Grunau, H.-Ch.:

L^p-decay rates for strong solutions of a perturbed Navier-Stokes system in R^3, in: J. G. Heywood, K. Masuda, R. Rautmann, V. A. Solonnikov (eds.),
Theory of the Navier-Stokes Equations, Series Adv. Math. Appl. Sciences 47, 64-71 (1998).

Grunau, H.-Ch., Sweers, G.:

The role of positive boundary data in generalized clamped plate equations,
Z. angew. Math. Phys., 49, 420-435 (1998).
[Ps] [Pdf] [Dvi]
Copyright: Birkhäuser-Verlag. The original article is available on http://link.springer.com/

Grunau, H.-Ch., Sweers, G.:

Maximum principles and positive principal eigenfunctions for polyharmonic equations, in: G. Caristi, E. Mitidieri (eds.),
Reaction Diffusion Systems, Lecture Notes in Pure and Applied Mathematics 194, 163-182 (1998).

Grunau, H.-Ch.:

Uniqueness of small solutions to the Dirichlet problem for the higher dimensional H-system,
Rocky Mountain J. Math. 27, 801-815 (1997).

Grunau, H.-Ch., Sweers, G.:

Positivity properties of elliptic boundary value problems of higher order,
Proc. 2nd World Congress of Nonlinear Analysis, Nonlinear Anal., T. M. A. 30, 5251-5258 (1997).

Grunau, H.-Ch., Wahl, W. von:

Regularity considerations for semilinear parabolic systems,
Rend. Istit. Mat. Univ. Trieste 28 (Suppl.), 221-233 (1997).

Grunau, H.-Ch., Sweers, G.:

Classical solutions for some higher order semilinear elliptic equations under weak growth conditions,
Nonlinear Anal., T.M.A. 28, 799-807 (1997).

Grunau, H.-Ch., Sweers, G.:

Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions,
Math. Ann. 307, 589-626 (1997).
[Ps] [Pdf] [Dvi]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Grunau, H.-Ch.:

On a conjecture of P. Pucci and J. Serrin,
Analysis 16, 399-403 (1996).
[Ps] [Pdf] [Dvi]
Copyright: de Gruyter http://www.degruyter.com

Grunau, H.-Ch., Sweers, G.:

Positivity for perturbations of polyharmonic operators with Dirichlet boundary conditions in two dimensions,
Math. Nachr. 179, 89-102 (1996).
[Ps] [Pdf] [Dvi]
Copyright: Mathematische Nachrichten, Wiley Verlag http://www.wiley-vch.de/

Grunau, H.-Ch.:

Critical exponents and multiple critical dimensions for polyharmonic operators. II,
Boll. Unione Mat. Ital. (7) 9-B, 815-847 (1995).

Grunau, H.-Ch.:

Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents,
Calculus of Variations and PDE 3, 243-252 (1995).

Bernis, F., Grunau, H.-Ch.:

Critical exponents and multiple critical dimensions for polyharmonic operators,
J. Differ. Equations 117, 469-486 (1995).

Grunau, H.-Ch., Wahl, W. von:

Regularity of weak solutions of semilinear parabolic systems of arbitrary order,
Journal d'Analyse 62, 307-322 (1994).
[Ps] [Pdf] [Dvi]

Grunau, H.-Ch.:

L^2-decay rates for weak solutions of a perturbed Navier-Stokes system in R^3,
J. Math. Anal. Appl. 185, 340-349 (1994).

Grunau, H.-Ch.:

The Reynolds number and large time behaviour for weak solutions of the Navier-Stokes equations,
Z. angew. Math. Phys. 44, 587-593 (1993).

Grunau, H.-Ch.:

Boundedness for large |x| of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity,
Commun. Math. Phys. 151, 577-587 (1993).
[Pdf]
Copyright: Springer-Verlag. The original article is available on http://link.springer.com/

Grunau, H.-Ch.:

The Dirichlet problem for some semilinear elliptic differential equations of arbitrary order,
Analysis 11, 83-90 (1991).