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Displaying 141 – 160 of 161

On the spectrum of the p-biharmonic operator involving p-Hardy's inequality

Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)

Applicationes Mathematicae

In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: ${Δ (| Δ u |}^{p - 2} {Δ u) = λ (| u |}^{p - 2} u) / (δ {(x)}^{2 p})$ in Ω, $u \in W ₀^{2, p} (Ω)$ . By using the variational technique and the Hardy-Rellich inequality, we prove that the above problem has at least one increasing sequence of positive eigenvalues.

On the spectrum of the reduced wave operators with cylindrical discontinuity.

Willi Jäger, Yoshimi Saito (1997)

Forum mathematicum

On the structure of the spectrum for the elasticity problem in a body with a supersharp spike.

Bakharev, F.L., Nazarov, S.A. (2009)

Sibirskij Matematicheskij Zhurnal

On the Uniform Decay of the Local Energy

Vodev, Georgi (1999)

Serdica Mathematical Journal

It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

On the uniqueness and simplicity of the principal eigenvalue

Marcello Lucia (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Given an open set $Ω$ of $R^{N}$ $(N > 2)$ , bounded or unbounded, and a function $w \in L^{\frac{N}{2}} (Ω)$ with $w^{+} \neq 0$ but allowed to change sign, we give a short proof...

On the Wave Equation on a Compact Riemannian Manifold withour Conjugate Points.

Pierre H. Bérard (1977)

Mathematische Zeitschrift

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Lorenzo Brasco (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We generalize to the p-Laplacian Δp a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of Δp of a set in terms of its p-torsional rigidity. The result is valid in every space dimension, for every 1 < p < ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants. The method of proof...

Opérateur de diffraction pour le système de Maxwell en métrique de Schwarzschild

Alain Bachelot (1990)

Journées équations aux dérivées partielles

Opérateur de Schrödinger avec champ magnétique

Yves Colin de Verdière, Nabila Torki (1992/1993)

Séminaire de théorie spectrale et géométrie

Opérateurs de convolution définis à partir d'une forme quadratique

Alain Bachelot (1982)

Journées équations aux dérivées partielles

Opérateurs de Schrödinger avec champ magnétique

B. Helffer (1986/1987)

Séminaire Équations aux dérivées partielles (Polytechnique)

Opérateurs de Schrödinger avec champs magnétiques faibles et constants

B. Helffer, J. Sjöstrand (1988/1989)

Séminaire Équations aux dérivées partielles (Polytechnique)

Opérateurs de temps-retard dans la théorie de la diffusion

Xue Ping Wang (1985)

Publications mathématiques et informatique de Rennes

Optimal energy decay rate of coupled wave equations.

Benaddi, Ahmed (2004)

Portugaliae Mathematica. Nova Série

Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains

Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2016)

Journal of the European Mathematical Society

We consider the wave and Schrödinger equations on a bounded open connected subset $Ω$ of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset $ω$ of $Ω$ during a time interval $[0, T]$ with $T > 0$ . It is well known that, if the pair $(ω, T)$ satisfies the Geometric Control Condition ( $ω$ being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be...

Optimal potentials for Schrödinger operators

Giuseppe Buttazzo, Augusto Gerolin, Berardo Ruffini, Bozhidar Velichkov (2014)

Journal de l’École polytechnique — Mathématiques

We consider the Schrödinger operator $- Δ + V (x)$ on $H_{0}^{1} (Ω)$ , where $Ω$ is a given domain of $ℝ^{d}$ . Our goal is to study some optimization problems where an optimal potential $V \geq 0$ has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.

Optimal Proliferation Rate in a Cell Division Model

P. Michel (2010)

Mathematical Modelling of Natural Phenomena

We consider a size structured cell population model where a mother cell gives birth to two daughter cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a...

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