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Outil de base dans les domaines des équations aux dérivées partielles et de l'analyse sur les variétés, les opérateurs pseudo- différentiels permettent de porter un regard neuf sur la méthode de perturbation de Nash et Moser. Analyse microlocale, théorie de Littlewood-Paley, inégalités d'énergie pour les équations hyperboliques et théorèmes de fonctions implicites sont abordés.

Pseudodifferential operators. --- Implicit functions. --- Functions, Implicit --- Functions of several real variables --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory

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The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. The first chapter of the book treats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomes gradually more advanced, and considers implicit mappings defined by relations other than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided. This valuable book is a major achievement and is sure to become a standard reference on the topic.

Implicit functions. --- Mappings (Mathematics). --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions, Implicit --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical optimization. --- Engineering economics. --- Engineering economy. --- Analysis. --- Optimization. --- Engineering Economics, Organization, Logistics, Marketing. --- Economy, Engineering --- Engineering economics --- Industrial engineering --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- 517.1 Mathematical analysis --- Math --- Science --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Functions of several real variables --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Implicit functions

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This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While the book gives many examples of the usefulness of the methods for a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems. The book begins with the description of implicit surfaces and their basic properties, and then devises the level set geometry and calculus toolbox, including the construction of signed distance functions. Part II adds dynamics to this static calculus. Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, reinitialization to a signed distance function, extrapolation in the normal direction, the particle level set method, and the motion of codimension two (and higher) objects. Part III is concerned with topics taken from the field of image processing and computer vision. These include the restoration of images degraded by noise and blur, image segmentation with active contours (snakes), and reconstruction of surfaces from unorganized data points. Part IV is dedicated to computational physics. It begins with one-phase compressible fluid dynamics, then two-phase compressible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incompressible fluid dynamics, including a computer graphics simulation of smoke; free surface flows, including a computer graphics simulation of water; and fully two-phase incompressible flow. Additional related topics include incompressible flames with applications to computer graphics and coupling a compressible and incompressible fluid. Finally, heat flow and Stefan problems are discussed. A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change it's topology or develop singularities, will find this book interesting and useful.

Level set methods. --- Implicit functions. --- Fonctions implicites --- Level set methods --- Implicit functions --- 514.8 --- 681.3*G18 --- Level sets (Mathematics) --- Osher-Sethian level set methods --- Sethian level set methods, Osher --- -Interfaces (Physical sciences) --- Functions, Implicit --- Functions of several real variables --- Geometric study of objects of mechanics and physics --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- Physics --- Atomic Physics --- Mathematical Theory --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 514.8 Geometric study of objects of mechanics and physics --- -Functions, Implicit --- Mathematics. --- Image processing. --- Computer mathematics. --- Continuum physics. --- Mechanics. --- Mechanics, Applied. --- Computational Mathematics and Numerical Analysis. --- Classical Continuum Physics. --- Image Processing and Computer Vision. --- Theoretical and Applied Mechanics. --- 681.3 *G18 --- Computer science --- Computer vision. --- Mechanics, applied. --- Classical and Continuum Physics. --- Optical data processing. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Classical field theory --- Continuum physics --- Continuum mechanics --- Computer mathematics --- Optical equipment --- Méthodes d'ensembles de niveaux --- Representation des surfaces