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Applications harmoniques entre graphes finis et un théorème de superrigidité

Édouard Lebeau (1996)

Annales de l'institut Fourier

Nous définissons une ntoion d’énergie pour des applications entre deux graphes métriques finis et cherchons à minimiser l’énergie au sein d’une classe d’homotopie. Nous démontrons des théorèmes d’existence et d’unicité analogues à ceux de Eells-Sampson et de Hartman pour les applications harmoniques à valeurs dans les variétés à courbure négative ou nulle. Nous montrons également une propriété de stabilité des applications minimisantes par rapport aux revêtements de degré fini à la source. Une application...

Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian

Kei Funano (2016)

Analysis and Geometry in Metric Spaces

We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.

Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition

Francine Meylan (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a complex Banach space. Recall that X admits afinite-dimensional Schauder decompositionif there exists a sequence { X n } n = 1 of finite-dimensional subspaces of X , such that every x X has a unique representation of the form x = n = 1 x n , with x n X n for every n . The finite-dimensional Schauder decomposition is said to beunconditionalif, for every x X , the series x = n = 1 x n , which represents x , converges unconditionally, that is, n = 1 x π ( n ) converges for every permutation π of the integers. For short, we say that X admits an unconditional F.D.D.We...

Approximation of the Heaviside function and uniqueness results for a class of quasilinear elliptic-parabolic problems.

G. Gagneux, F. Guerfi (1990)

Revista Matemática de la Universidad Complutense de Madrid

In this paper, we concern ourselves with uniqueness results for an elliptic-parabolic quasilinear partial differential equation describing, for instance, the pressure of a fluid in a three-dimensional porous medium: within the frame of mathematical modeling of the secondary recovery from oil fields, the handling of the component conservation laws leads to a system including such a pressure equation, locally elliptic or parabolic according to the evolution of the gas phase.

Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems

Marek Izydorek, Joanna Janczewska (2014)

Banach Center Publications

In this work we will consider a class of second order perturbed Hamiltonian systems of the form q ̈ + V q ( t , q ) = f ( t ) , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained...

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