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Given a Hörmander system $X = {X_{1}, \dots, X_{m}}$ on a domain $Ω \subseteq 𝐑^{n}$ we show that any subelliptic harmonic morphism $φ$ from $Ω$ into a $ν$ -dimensional riemannian manifold $N$ is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also $φ$ is a submersion provided that $ν \leq m$ and $X$ has rank $m$ . If $Ω = 𝐇_{n}$ (the Heisenberg group) and $X = \{\frac{1}{2} (L_{α} + L_{\bar{α}}), \frac{1}{2 i} (L_{α} - L_{\bar{α}})\}$ , where $L_{\bar{α}} = \partial / \partial {\bar{z}}^{α} - i z^{α} \partial / \partial t$ is the Lewy operator, then a smooth map $φ : Ω \to N$ is a subelliptic harmonic morphism if and only if $φ \circ π : (C (𝐇_{n}), F_{θ_{0}}) \to N$ is a harmonic morphism, where $S^{1} \to C (𝐇_{n}) \overset{π}{\to} \to 𝐇_{n}$ is the canonical circle bundle and $F_{θ_{0}}$ is the Fefferman...

Hybrid robust stabilization in the Martinet case

Christophe Prieur, Emmanuel Trélat (2006)

Control and Cybernetics

Hyperbolic characteristics on star-shaped hypersurfaces

Chun-Gen Liu, Yiming Long (1999)

Annales de l'I.H.P. Analyse non linéaire

Hypersurfaces with Constant Mean Curvature and Prescribed Area.

Frank Duzaar (1996)

Manuscripta mathematica

Improved estimates for the Ginzburg-Landau equation : the elliptic case

Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the $G L$ -energy $E_{ε}$ and the parameter $ε$ . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

Impulsive boundary value problems for $p (t)$ -Laplacian’s via critical point theory

Marek Galewski, Donal O'Regan (2012)

Czechoslovak Mathematical Journal

In this paper we investigate the existence of solutions to impulsive problems with a $p (t)$ -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...

Index and stability of harmonic Gauss maps.

Bennett Palmer (1991)

Mathematische Zeitschrift

Indice de Morse des applications harmoniques de la sphère

Ahmad El Soufi (1995)

Compositio Mathematica

Indice de Morse des applications p-harmoniques

Ahmad El Soufi, Albert Jeune (1996)

Annales de l'I.H.P. Analyse non linéaire

Indice de Morse des points critiques obtenus par minimax

Claude Viterbo (1988)

Annales de l'I.H.P. Analyse non linéaire

Inégalités de Morse pour la $d^{''}$ -cohomologie sur une variété holomorphe non compacte

Thierry Bouche (1989)

Annales scientifiques de l'École Normale Supérieure

Inégalités variationnelles non convexes

Messaoud Bounkhel, Djalel Bounkhel (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d’inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.

Inégalités variationnelles non convexes

Messaoud Bounkhel, Djalel Bounkhel (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d'inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée.

Infinite cup length in free loop spaces with an application to a problem of the N-body type

E. Fadell, S. Husseini (1992)

Annales de l'I.H.P. Analyse non linéaire

Infinite geodesic rays in the space of Kähler potentials

Claudio Arezzo, Gang Tian (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the...

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