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Marie-France VIGNERAS (1981/1982)

Seminaire de Théorie des Nombres de Bordeaux

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

A Hörmander-type spectral multiplier theorem for operators without heat kernel

Sönke Blunck (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hörmander’s famous Fourier multiplier theorem ensures the L p -boundedness of F ( - Δ D ) whenever F ( s ) for some s > D 2 , where we denote by ( s ) the set of functions satisfying the Hörmander condition for s derivatives. Spectral multiplier theorems are extensions of this result to more general operators A 0 and yield the L p -boundedness of F ( A ) provided F ( s ) for some s sufficiently large. The harmonic oscillator A = - Δ + x 2 shows that in general s > D 2 is not sufficient even if A has a heat kernel satisfying gaussian estimates. In this paper,...

A lower bound for the principal eigenvalue of the Stokes operator in a random domain

V. V. Yurinsky (2008)

Annales de l'I.H.P. Probabilités et statistiques

This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...

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