Chaire d'analyse mathématique et applications CAA

Livres de B. Dacorogna

Direct Methods in the Calculus of Variations

2ème édition

1ère édition épuisée

This book studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added. This monograph will appeal to researchers and graduate students in mathematics and engineering.

Introduction to the Calculus of Variations

3ème édition
version anglaise

2ème édition
version anglaise

1ère édition
version anglaise

version française

The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.
This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subject’s most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.
In this new edition, several new exercises have been added. The book,containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.

The Pullback Equation for Differential Forms

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem under considersation is therefore to find a map so that it satisfies the pullback equation

The Pullback Equation for Differential Forms is a self contained and concise monograph intended for both geometers and analysts. The book can serve as a valuable reference for researchers or a supplemental text for graduate students.

Implicit Partial Differential Equations

Nonlinear partial differential equations has become one of the main tools of mod­ ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nonlinear equations, particularly those of the second order, both linear and nonlinear and either in divergence or nondivergence form. Quasilinear and fully nonlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called "implicit partial differential equations", described in detail in the introduction (c.f. Chapter 1). It is a class of nonlinear equations that does not include the family of fully nonlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nonlin­ ear elasticity, problems of phase transitions and optimal design; some results have not been published elsewhere.

Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals


This book is concerned with the theory of compensated compactness with applications to partial differential equations and the calculus of variations.

E-book only available.

Analyse avancée pour ingénieurs (version française)

La matière traitée dans cet ouvrage comprend l’analyse vectorielle (théorèmes de Green, de la divergence, de Stokes), l'analyse complvexe (fonctions holomorphes, équations de Cauchy-Riemann, séries de Laurent, théorème des résidus, applications conformes) ainsi que l'analyse de Fourier (séries de Fourier, transformées de Fourier, transformées de Laplace, applications aux équations différentielles). Les définitions et les théorèmes principaux sont présentés sous forme d’aide-mémoire, énoncés avec clarté et précision sans commentaires. De très nombreux exemples significatifs sont ensuite discutés en détail. Enfin, de nombreux exercices corrigés sont proposés intégralement.

Mathematical Analysis for Engineers (version anglaise)

This book follows an advanced course in analysis (vector analysis, complex analysis and Fourier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students.

The first three parts of the book represent the theoretical aspect and are independent of each other. The fourth part gives detailed solutions to all exercises that are proposed in the first three parts.

Calculus of Variations and Non-Linear Partial Differential Equations

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.
Edited by B. Dacorogna and P. Marcellini.

Contacts CAA

Bernard Dacorogna

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Tél: +41 (0) 21 693 21 93
Fax: +41 (0) 21 693 58 39