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Displaying 161 – 180 of 180

Weyl type upper bounds on the number of resonances near the real axis for trapped systems

Plamen Stefanov (2001)

Journées équations aux dérivées partielles

We study semiclassical resonances in a box $Ω (h)$ of height $h^{N}$ , $N ≫ 1$ . We show that the semiclassical wave front set of the resonant states (including the “generalized eigenfunctions”) is contained in the set $𝒯$ of the trapped bicharacteristics. We also show that for a suitable self-adjoint reference operator $P^{#} (h)$ with discrete spectrum the number of resonances in $Ω (h)$ is bounded by the number of eigenvalues of $P^{#} (h)$ in an interval a bit larger than the projection of $Ω (h)$ on the real line. As an application, we prove a...

What is the smallest possible constant in Céa's lemma?

Wei Chen, Michal Křížek (2006)

Applications of Mathematics

We consider finite element approximations of a second order elliptic problem on a bounded polytopic domain in $ℝ^{d}$ with $d \in {1, 2, 3, ...}$ . The constant $C \geq 1$ appearing in Céa’s lemma and coming from its standard proof can be very large when the coefficients of an elliptic operator attain considerably different values. We restrict ourselves to regular families of uniform partitions and linear simplicial elements. Using a lower bound of the interpolation error and the supercloseness between the finite element solution and...

When does the free boundary enter into corner points of the fixed boundary?

Shahgholian, H. (2004)

Zapiski Nauchnykh Seminarov POMI

When is a pseudo-differential equation solvable ?

Nicolas Lerner (2000)

Annales de l'institut Fourier

This paper begins with a broad survey of the state of the art in matters of solvability for differential and pseudo-differential equations. Then we proceed with a Hilbertian lemma which we use to prove a new solvability result.

When is the first eigenfunction for the clamped plate equation of fixed sign?

Sweers, Guido (2001)

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

Which electric fields are realizable in conducting materials?

Marc Briane, Graeme W. Milton, Andrejs Treibergs (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we study the realizability of a given smooth periodic gradient field ∇u defined in Rd, in the sense of finding when one can obtain a matrix conductivity σ such that σ∇u is a divergence free current field. The construction is shown to be always possible locally in Rd provided that ∇u is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fact the realizability may fail for non-regular gradient fields, and in general the conductivity cannot...

Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?

Alain Damlamian, Patrizia Donato (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that $H^{0}$ -convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result applies....

Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?

Alain Damlamian, Patrizia Donato (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we give a general presentation of the homogenization of Neumann type problems in periodically perforated domains, including the case where the shape of the reference hole varies with the size of the period (in the spirit of the construction of self-similar fractals). We shows that H0-convergence holds under the extra assumption that there exists a bounded sequence of extension operators for the reference holes. The general class of Jones-domains gives an example where this result...

Which solutions of the third problem for the Poisson equation are bounded?

Medková, Dagmar (2004)

Abstract and Applied Analysis

Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law

Blake Barker, Mathew A. Johnson, Pascal Noble, L.Miguel Rodrigues, Kevin Zumbrun (2010)

Journées Équations aux dérivées partielles

In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow down an incline. We begin by introducing a natural set of spectral stability assumptions, motivated by considerations from the Whitham averaged equations, and outline the recent proof yielding nonlinear stability under these conditions. We then turn to an analytical...

Whitney elements on pyramids.

Gradinaru, V., Hiptmair, R. (1999)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Wiener criterion for degenerate elliptic obstacle problem

Marco Biroli, Umberto Mosco (1989)

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

We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the $A_{2}$ class.

Wiener type algebras of pseudodifferential operators

J. Sjöstrand (1994/1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

Wiener's Criterion in Potential Theory with Applications to Nilpotent Lie Groups.

H. Hueber (1985)

Mathematische Zeitschrift

Wiener's test of thinness in potential theory

Miroslav Brzezina (1990)

Commentationes Mathematicae Universitatis Carolinae

Wigner series and (semi)classical limits with periodic potentials

Peter A. Markowich, Norbert J. Mauser, Frédéric Poupaud (1993)

Journées équations aux dérivées partielles

WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity

Thomas Alazard, Rémi Carles (2009)

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

Wm,2-Fehlerabschätzungen für Galerkin-Näherungen schwach elliptischer quasilinearer Randwertprobleme 2m-ter Ordnung.

R. Kosler (1985)

Numerische Mathematik

Worst scenario method in homogenization. Linear case

Luděk Nechvátal (2006)

Applications of Mathematics

The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized...

Wüst's Theorem and Positively Perturbed Schrödinger Operators.

Herbert Leinfelder (1980)

Mathematische Zeitschrift

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