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Displaying 121 – 140 of 334

Energy and Morse index of solutions of Yamabe type problems on thin annuli

Mohammed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou, Filomena Pacella (2005)

Journal of the European Mathematical Society

We consider the Yamabe type family of problems $(P_{ε}) : - Δ u_{ε} = u_{ε}^{(n + 2) / (n - 2)}$ , $u_{ε} > 0$ in $A_{ε}$ , $u_{ε} = 0$ on $\partial A_{ε}$ , where $A_{ε}$ is an annulus-shaped domain of $ℝ^{n}$ , $n \geq 3$ , which becomes thinner as $ε \to 0$ . We show that for every solution $u_{ε}$ , the energy $\int_{A_{ε}} | \nabla u_{|}^{2}$ as well as the Morse index tend to infinity as $ε \to 0$ . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on $ℝ^{n}$ , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...

Energy concentration for the Landau–Lifshitz equation

Roger Moser (2008)

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

Energy machineries on a manifold; application to the construction of new energy representations of Gauge groups.

Jean-Yves Marion (1990)

Publicacions Matemàtiques

The introduction of the concepts of energy machinery and energy structure on a manifold makes it possible a large class of energy representations of gauge groups including, as a very particular case, the ones known up to now. By using an adaptation of methods initiated by I. M. Gelfand, we provide a sufficient condition for the irreducibility of these representations.

Energy quantization for Yamabe's problem in conformal dimension.

Mahmoudi, Fethi (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Engel structures with trivial characteristic foliations.

Adachi, Jiro (2002)

Algebraic & Geometric Topology

Engouffrement symplectique et intersections lagrangiennes.

Francois Laudenbach (1995)

Commentarii mathematici Helvetici

Entire Spacelike Hypersurfaces on Constant Mean Curvature in Minkowski Space.

Andrejs E. Treibergs (1982)

Inventiones mathematicae

Entire spacelike radial graphs in the Minkowski space, asymptotic to the light-cone, with prescribed scalar curvature

Pierre Bayard, Philippe Delanoë (2009)

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

Entropies des flots magnétiques

Stéphane Grognet (1999)

Annales de l'I.H.P. Physique théorique

Entropies et rigidité des espaces localement symétriques de courbure strictement.

S. Gallot, G. Besson, G. Courtois (1995)

Geometric and functional analysis

Entropy and complexity of a path in sub-riemannian geometry

Frédéric Jean (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset $A$ of a metric space is the minimum number of balls of a given radius $ε$ needed to cover $A$ . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an $ε$ -neighborhood of the path,...

Entropy and complexity of a path in sub-Riemannian geometry

Frédéric Jean (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...

Entropy of eigenfunctions of the Laplacian in dimension 2

Gabriel Rivière (2010)

Journées Équations aux dérivées partielles

We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [4] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure $μ$ for the geodesic flow $g^{t}$ is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the $37^{èmes}$ Journées EDP (Port d’Albret-June, 7-11 2010))

Entropy of Geodesic Flow and Exponent of Convergence of Some Dirichlet Series.

Su-shing Chen (1981)

Mathematische Annalen

Envelopes -- notion and definiteness.

Kock, Anders (2007)

Beiträge zur Algebra und Geometrie

Enveloppe galoisienne d'une application rationnelle de P1.

Guy Casale (2006)

Publicacions Matemàtiques

In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.

Epsilon Nielsen coincidence theory

Marcio Fenille (2014)

Open Mathematics

We construct an epsilon coincidence theory which generalizes, in some aspect, the epsilon fixed point theory proposed by Robert Brown in 2006. Given two maps f, g: X → Y from a well-behaved topological space into a metric space, we define µ ∈(f, g) to be the minimum number of coincidence points of any maps f 1 and g 1 such that f 1 is ∈ 1-homotopic to f, g 1 is ∈ 2-homotopic to g and ∈ 1 + ∈ 2 < ∈. We prove that if Y is a closed Riemannian manifold, then it is possible to attain µ ∈(f, g) moving...

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