Publikationen

Optimality of smallness conditions in willmore obstacle problems under dirichlet boundary conditions

Grunau, Hans-Christoph; Okabe, Shinya

In: Nonlinear analysis. Real world applications - Amsterdam [u.a.] : Elsevier Science, Bd. 85 (2025), insges. 10 S.

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A biharmonic analogue of the Alt–Caffarelli problem

Grunau, Hans-Christoph; Müller, Marius

In: Mathematische Annalen - Berlin : Springer, Bd. 390 (2024), Heft 4, S. 5259-5297

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Willmore boundary value problems

Gulyak, Boris; Grunau, Hans-Christoph

In: Magdeburg: Universitätsbibliothek, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2024, 1 Online-Ressource (201 Seiten, 1,41 MB) [Literaturverzeichnis: Seite 192-201][Literaturverzeichnis: Seite 192-201]

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Willmore obstacle problems under dirichlet boundary conditions

Grunau, Hans-Christoph; Okabe, Shinya

In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze - Pisa : Scuola Normale Superiore, Bd. 24 (2023), Heft 3, S. 1415-1462

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Willmore obstacle problems under Dirichlet boundary conditions

Grunau, Hans-Christoph; Okabe, Shinya

In: De.arxiv.org - [Erscheinungsort nicht ermittelbar] : Arxiv.org . - 2023, Artikel 2103.15382, insges. 36 S.

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Optimal estimates from below for Green functions of higher order elliptic operators with variable leading coefficients

Grunau, Hans-Christoph

In: Archiv der Mathematik - Berlin: Springer, Bd. 117 (2021), S. 95-104

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Boundary value problems for a special Helfrich functional for surfaces of revolution - existence and asymptotic behaviour

Deckelnick, Klaus; Doemeland, Marco; Grunau, Hans-Christoph

In: Calculus of variations and partial differential equations - Berlin: Springer, Bd. 60 (2021), insges. 31 S.

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Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators

Grunau, Hans-Christoph; Romani, Giulio; Sweers, Guido

In: Mathematische Annalen - Berlin: Springer, 1869 . - 2020

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Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations

Grunau, Hans-Christoph; Miyake, Nobuhito; Okabe, Shinya

In: Advances in nonlinear analysis - Berlin : de Gruyter, Bd. 10 (2020), Heft 1, S. 353-370

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Boundary value problems for the Willmore functional

Grunau, Hans-Christoph

In: Magdeburg: Universität, Fakultät für Mathematik, 2018, 17 Seiten, Diagramme - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2018,Nr.04)

Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions

Eichmann, Sascha; Grunau, Hans-Christoph

In: Advances in calculus of variations - Berlin : de Gruyter, 2017

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Minimising a relaxed Willmore functional for graphs subject to boundary conditions

Deckelnick, Klaus; Grunau, Hans-Christoph; Röger, Matthias

In: Interfaces and free boundaries - Zürich : European Mathematical Soc. Publ. House, Bd. 19 (2017), Heft 1, S. 109-140

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Boggio’s formula for fractional polyharmonic Dirichlet problems

Dipierro, Serena; Grunau, Hans-Christoph

In: Annali di matematica pura ed applicata - Berlin : Springer . - 2016, insges. 18 S.

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Jahresbericht der Deutschen Mathematikervereinigung

Grunau, Hans-Christoph

In: 2016

Dominance of positivity of the Green's function associated to a perturbed polyharmonic dirichlet boundary value problem by pointwise estimates

Pulst, Ludwig; Grunau, Hans-Christoph

In: Magdeburg, Univ., Fak. für Mathematik, Diss., 2015, 95 S., graph. Darst.

Jahresbericht der Deutschen Mathematiker-Vereinigung

Grunau, Hans-Christoph

In: 2015

In any dimension a “clamped plate” with a uniform weight may change sign

Grunau, Hans-Christoph; Sweers, Guido

In: Nonlinear analysis - an international multidisciplinary journal - Amsterdam [u.a.] : Elsevier, Pergamon Press, Bd. 97 (2014), S. 119-124

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A clamped plate with a uniform weight may change sign

Grunau, Hans-Christoph; Sweers, Guido

In: Discrete and continuous dynamical systems - Springfield, Mo. : American Institute of Mathematical Sciences, Bd. 7 (2014), Heft 7, S. 761-766

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Uniform estimates and convexity in capillary surfaces

Grunau, Hans-Christoph; Lenor, Stephan

In: Nonlinear analysis - an international multidisciplinary journal - Amsterdam [u.a.] : Elsevier, Pergamon Press, Bd. 97 (2014), S. 83-93

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Uniform estimates for polyharmonic Green functions in domains with small holes

Grunau, Hans-Christoph; Robert, Frédéric

In: Recent trends in nonlinear partial differential equations II. - Providence, Rhode Island : American Mathematical Society, S. 263-272, 2013Kongress: Workshop on nonlinear partial differential equations; (Perugia, Italy) : 2012

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The asymptotic shape of a boundary layer of symmetric willmore surfaces of revolution

Grunau, Hans-Christoph

In: Inequalities and applications 2010. - Basel [u.a.] : Birkhäuser [u.a.], S. 19-29, 2012 - (International series of numerical mathematics; 161)Kongress: Conference on Inequalities and Applications; 2 (Hajdúszoboszló, Hungary) : 2010.09.

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Optimal estimates from below for biharmonic Green functions

Grunau, Hans-Christoph; Robert, Frédéric; Sweers, Guido

In: Proceedings of the American Mathematical Society. - Providence, RI : Soc, Bd. 139.2011, 6, S. 2151-2161

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Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data

Dall'Acqua, Anna; Fröhlich, Steffen; Grunau, Hans-Christoph; Schieweck, Friedhelm

In: Advances in calculus of variations - Berlin : ˜deœ Gruyter, Bd. 4 (2011), Heft 1, S. 1-81

Optimal Sobolev and Hardy Rellich constants under navier boundary conditions

Gazzola, Filippo; Grunau, Hans-Christoph; Sweers, Guido

In: Annali di matematica pura ed applicata - Heidelberg : Springer, Bd. 189 (2010), Heft 3, S. 475-486

Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions

Grunau, Hans-Christoph; Robert, Frédéric

In: Archive for rational mechanics and analysis . - Berlin : Springer, Bd. 195.2010, 3, S. 865-898

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Polyharmonic boundary value problems - positivity preserving and nonlinear higher order elliptic equations in bounded domains

Gazzola, Filippo; Grunau, Hans-Christoph; Sweers, Guido

In: Heidelberg [u.a.]: Springer, 2010, XVIII, 423 S. - (Lecture notes in mathematics; 1991), ISBN: 978-3-642-12244-6 [Literaturverz. S. 397 - 413]

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A Navier boundary value problem for Willmore surfaces of revolution

Deckelnick, Klaus; Grunau, Hans-Christoph

In: Analysis - Berlin : ˜deœ Gruyter, Oldenbourg Wissenschaftsverl., Bd. 29 (2009), Heft 3, S. 229-258

Nonlinear questions in clamped plate models

Grunau, Hans-Christoph

In: Milan journal of mathematics - Cham (ZG) : Springer International Publishing AG, Bd. 77 (2009), Heft 1, S. 171-204

Stability and symmetry in the Navier problem for the one-dimensional Willmore equation

Deckelnick, Klaus; Grunau, Hans-Christoph

In: SIAM journal on mathematical analysis / Society for Industrial and Applied Mathematics - Philadelphia, Pa. : SIAM, Bd. 40 (2009), Heft 5, S. 2055-1076

Boundedness of the negative part of biharmonic Greens functions under dirichlet boundary conditions in general domains

Grunau, Hans-Christoph; Robert, Frédéric

In: Comptes rendus mathematique . - Paris : Elsevier, Bd. 347.2009, 3/4, S. 163-166

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Some new proberties of biharmonic heat kernels

Gazzola, Filippo; Grunau, Hans-Christoph

In: Nonlinear analysis . - Oxford : Pergamon, Elsevier Science, ISSN 0362-546x, Bd. 70.2009, 8, S. 2965-2973

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Decay and local eventual positivity for biharmonic parabolic equations

Ferrero, Alberto; Gazzola, Filippo; Grunau, Hans-Christoph

In: Discrete and continuous dynamical systems / S. - Springfield, Mo, Bd. 1.2008, 4, S. 1129-1157

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The second bifurcation branch for radial solutions of the Brezis-Nirenberg problem in dimension four

Arioli, Gianni; Gazzola, Filippo; Grunau, Hans-Christoph; Sassone, Edoardo

In: Nonlinear differential equations and applications: Nodea : Nodea - [Cham (ZG)] : [Springer International Publishing AG], Bd. 15 (2008), 1/2, S. 69-90

The Paneitz equation in hyperbolic space

Grunau, Hans-Christoph; Ahmedou, Mohameden Ould; Reichel, Wolfgang

In: Annales de l'Institut Henri Poincaré. C, Analyse non-linéaire - Berlin : European Mathematical Society - EMS, Bd. 25 (2008), Heft 5, S. 847-864

Supercritical biharmonic equations with power-type nonlinearity

Ferrero, Alberto; Grunau, Hans-Christoph; Karageorgis, Paschalis

In: Annali di matematica pura ed applicata - Heidelberg : Springer, Bd. 188 (2009), Heft 1, S. 171-185

Eventual local positivity for a biharmonic heat equation in R^n

Gazzola, Filippo; Grunau, Hans-Christoph

In: Discrete and continuous dynamical systems . - Springfield, Mo., Bd. 1.2008, 1, S. 83-87

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Classical solutions to the dirichlet problem for Willmore surfaces of revolution

Dall'Acqua, Anna; Deckelnick, Klaus; Grunau, Hans-Christoph

In: Advances in calculus of variations. - Berlin : de Gruyter, Bd. 1.2008, 4, S. 379-397

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Boundary value problems for the one-dimensional Willmore equation

Deckelnick, Klaus; Grunau, Hans-Christoph

In: Calculus of variations and partial differential equations - Berlin: Springer, Bd. 30 (2007), 3, S. 293-314

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Local regularity of weak solutions of semilinear parabolic systems with critical growth

Berchio, Elvise; Grunau, Hans-Christoph

In: Journal of evolution equations - Basel [u.a.]: Birkhäuser, Bd. 7 (2007), 1, S. 177-196

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The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity

Ferrero, Alberto; Grunau, Hans-Christoph

In: Journal of differential equations - Orlando, Fla.: Elsevier, Bd. 234 (2007), 2, S. 582-606

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Boundary value problems for the one-dimensional Willmore equation

Deckelnick, Klaus; Grunau, Hans-Christoph

In: Calculus of variations and partial differential equations - Berlin : Springer, Bd. 30 (2007), Heft 3, S. 293-314

The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity

Ferrero, Alberto; Grunau, Hans-Christoph

In: Journal of differential equations - Orlando, Fla. : Elsevier, Bd. 234 (2007), Heft 2, S. 582-606

Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay

Gazzola, Filippo; Grunau, Hans-Christoph

In: Calculus of variations and partial differential equations - Berlin: Springer, Bd. 30 (2007), 3, S. 389-415

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Local regularity of weak solutions of semilinear parabolic systems with critical growth

Berchio, Elvise; Grunau, Hans-Christoph

In: Journal of evolution equations - Basel [u.a.] : Birkhäuser, Bd. 7 (2007), Heft 1, S. 177-196

Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay

Gazzola, Filippo; Grunau, Hans-Christoph

In: Calculus of variations and partial differential equations - Berlin : Springer, Bd. 30 (2007), Heft 3, S. 389-415

Regions of positivity for polyharmonic green functions in arbitrary domains

Grunau, Hans-Christoph; Sweers, Guido

In: Proceedings of the American Mathematical Society - Providence, RI : Soc., Bd. 135 (2007), Heft 11, S. 3537-3546

Regions of positivity for polyharmonic green functions in arbitrary domains

Grunau, Hans-Christoph; Sweers, Guido

In: Proceedings of the American Mathematical Society/ American Mathematical Society - Providence, RI: Soc., Bd. 135 (2007), 11, S. 3537-3546

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Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity

Arioli, Gianni; Gazzola, Filippo; Grunau, Hans-Christoph

In: Journal of differential equations - Orlando, Fla. : Elsevier, Bd. 230 (2006), Heft 2, S. 743-770

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Radial entire solutions for supercritical biharmonic equations

Gazzola, Filippo; Grunau, Hans-Christoph

In: Mathematische Annalen - Berlin : Springer, Bd. 334 (2006), Heft 4, S. 905-936

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A semilinear fourth order elliptic problem with exponential nonlinearity.

Arioli, Gianni; Gazzola, Filippo; Grunau, Hans-Christoph; Mitidieri, Enzo

In: SIAM Journal on mathematical analysis [Philadelphia] 36(2005), Nr. 4, S. 1226 - 1258

On the existence of hermitian-harmonic maps from complete hermitian to complete Riemannian manifolds.

Grunau, Hans-Christoph; Kuehnel, Marco

In: Mathematische Zeitschrift [Berlin [u.a.]] 249(2005), S. 297 - 327

On a conditioned brownian motion and a maximum principle on the disk.

Dall'acqua, A.; Grunau, Hans-Christoph; Sweers, G.H.

In: Journal d'analyse mathématique [Jerusalem] 93(2004), S. 309 - 329

Hardy inequalities with optimal constants and remainder terms.

Gazzola, Filippo; Grunau, Hans-Christoph; Mitidieri, Enzo

In: Transactions of the American Mathematical Society [Providence, RI] 356(2004), Nr. 6, S. 2149 - 2168

Existence and nonexistence results for critical growth biharmonic elliptic equations.

Gazzola, Filippo; Grunau, Hans-Christoph; Squassina, Marco

In: Calculus of variations [Berlin] 18(2003), S. 117 - 143

Nonexistence of local minima of supersolutions for the circular clamped plate.

Grunau, Hans-Christoph; Sweers, Guido

In: Pacific journal of mathematics [Berkeley] 198(2001), Nr. 2, S. 437 - 442

Critical dimensions and higher order Sobolev inequalities with remainder terms.

Gazzola, Filippo; Grunau, Hans-Christoph

In: Nonlinear differential equations and applications : NoDEA [Basel] 8(2001), S. 35 - 44