/pdf/asymptotic-analysis-of-periodic-structures-14wjonu4ba.pdf

Asymptotic Analysis of Periodic Structures

A characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method, the point is to obtain compactness in a space Lp (0,T; B) from estimates with values in some spaces X, Y or B where X⊂B⊂Y with compact imbedding X→B. Using the present characterization for this kind of situations, sufficient conditions for compactness are given with optimal parameters. As an example, it is proved that if {fn} is bounded in Lq(0,T; B) and in L
 loc
 1
 (0, T; X) and if {∂fn/∂t} is bounded in L
 loc
 1
 (0, T; Y) then {fn} is relatively compact in Lp(0,T; B), ∀p<q.

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Compact sets in the spaceL p (O,T; B)

Notation.- Notation.- Gradient Flow in Metric Spaces.- Curves and Gradients in Metric Spaces.- Existence of Curves of Maximal Slope and their Variational Approximation.- Proofs of the Convergence Theorems.- Uniqueness, Generation of Contraction Semigroups, Error Estimates.- Gradient Flow in the Space of Probability Measures.- Preliminary Results on Measure Theory.- The Optimal Transportation Problem.- The Wasserstein Distance and its Behaviour along Geodesics.- Absolutely Continuous Curves in p(X) and the Continuity Equation.- Convex Functionals in p(X).- Metric Slope and Subdifferential Calculus in (X).- Gradient Flows and Curves of Maximal Slope in p(X).

Gradient Flows: In Metric Spaces and in the Space of Probability Measures

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Convexity conditions and existence theorems in nonlinear elasticity

Semi-martingales sur des variétés, et martingales conformes sur des variétés analytiques complexes

© Annales de l’université de Grenoble, 1945, tous droits réservés. L’accès aux archives de la revue « Annales de l’université de Grenoble » implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

/pdf/generalisation-de-la-notion-de-fonction-de-derivation-de-49f6xr9yw4.pdf

Généralisation de la notion de fonction, de dérivation, de transformation de Fourier et applications mathématiques et physiques

Lectures on mixed problems in partial differential equations and representations of semi-groups

Introduction: The Garden of Eden.- I The Revelation of Mathematics.- II A Student at the Ecole Normale Superieure in Love.- III Trotskyist.- IV A Researcher in the War.- V The War Against the Jews.- VI The Invention of Distributions.- VII Militating, Teaching, Research.- VIII International Recognition.- IX The Algerian Involvement.- X For an Independent Viet-Nam.- XI The Distant War in Afghanistan.- XII The Committee of Mathematicians.

A Mathematician Grappling with His Century

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Laurent Schwartz

Papers

Semi-martingales sur des variétés, et martingales conformes sur des variétés analytiques complexes

Généralisation de la notion de fonction, de dérivation, de transformation de Fourier et applications mathématiques et physiques

Lectures on mixed problems in partial differential equations and representations of semi-groups

A Mathematician Grappling with His Century

Un mathématicien aux prises avec le siècle