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Book Description
ON ETUDIE DES PROBLEMES NON LINEAIRES D'ORIGINE GEOMETRIQUE. POUR RESOUDRE LES EQUATIONS AUX DERIVEES PARTIELLES QUI EN SONT LA TRADUCTION ANALYTIQUE ON PRECISE CERTAINES INEGALITES CONCERNANT LES ESPACES DE SOBOLEV ET ON DETERMINE LES MEILLEURES CONSTANTES DANS CES INEGALITES. ON ENONCE DES THEOREMES DE TRACE SUR DES SOUS-VARIETES DE CODIMENSION >1
Book Description
ON ETUDIE DES PROBLEMES NON LINEAIRES D'ORIGINE GEOMETRIQUE. POUR RESOUDRE LES EQUATIONS AUX DERIVEES PARTIELLES QUI EN SONT LA TRADUCTION ANALYTIQUE ON PRECISE CERTAINES INEGALITES CONCERNANT LES ESPACES DE SOBOLEV ET ON DETERMINE LES MEILLEURES CONSTANTES DANS CES INEGALITES. ON ENONCE DES THEOREMES DE TRACE SUR DES SOUS-VARIETES DE CODIMENSION >1
Author: Thierry Aubin Publisher: Springer Science & Business Media ISBN: 9783540607526 Category : Mathematics Languages : en Pages : 422
Book Description
This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.
Author: Abdellah Hanani Publisher: ISBN: Category : Languages : en Pages : 352
Book Description
Les travaux qui font l'objet de cette habilitation sont consacrés à la résolution de divers problèmes non linéaires sur des variétés réelles ou complexes faisant appel à la théorie des équations aux dérivées partielles elliptiques non linéaires. Ces équations, du type Monge-Ampère ou quasilinéaire, sont selon les cas régulières ou dégénérées et apparaissent comme une traduction analytique de questions liées à la géométrie des variétés différentielles. En premier lieu, on étudie des équations du type de Monge-Ampère sur une variété hermitienne compacte avec ou sans bord. Dans le cas où la frontière est non vide, on suppose l'existence d'une fonction définissante partout strictement plurisousharmonique et on impose une condition au bord de type Dirichlet. Ensuite on s'est consacré à l'étude d'un problème de Neumann pour une équation pu type de Monge-Ampère réelle sur une variété Riemannienne compacte orientée et dont le bord est une hypersurface admettant une fonction définissante partout strictement convexe. Sous des hypothèses naturelles sur les données du problème, on montre que l'existence d'une sur solution est une condition nécéssaire et suffisante pour l'existence d'une solution du problème. La dernière partie traite le problème d'existence d'hypersurfaces dont on prescrit une fonction de courbure. Il s'agit d'une généralisation au cas d'un fibré vectoriel Riemannien de résultats établis dans le cadre Euclidien relatifs à l'existence de graphes radiaux à courbures moyenne ou de Gauss prescrites. La nature du cadre envisagé ici nous a permis de définir d'autres notions ge courbures comme les courbures moyennes verticale ou horizontale ou la courbure de Gauss verticale et d'étudier le problème d'existence de graphes radiaux dont on prescrit l'une de ces courbures; les équations à résoudre sont selon le cas quasilinéaires ou du type Monge- Ampère dégénérées.
Author: Thierry Aubin Publisher: Springer Science & Business Media ISBN: 1461257344 Category : Mathematics Languages : en Pages : 215
Book Description
This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.
Author: Philippe Choné Publisher: ISBN: Category : Languages : en Pages : 189
Book Description
In the first part of this thesis, we consider a critical point u of a conformally invariant functional on a two-dimensional domain. We show that if u is a priori assumed to be bounded, then u is smooth up to the boundary of the domain. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three dimensional compact Riemannian manifold. The variational problems studied in the second part are motivated by economic issues, namely non-linear pricing by a monopolist or a duopolist. The problem consists in maximizing a functional over the cone of convex functions. We give a sufficient condition for the convexity constraint to be active. This condition does hold in many common situations in economics. Typically, in a two-dimensional problem, there exists an area where the rank of the hessian of the solution is 1. We write the Euler equation of the problem and derive the + sweeping conditions. We explain how to use these conditions to compute the solution. This method, however, requires some prior knowledge of the solution. We therefore study the numerical approximation of the problem. We show how to apply some simple finite-elements methods to the problem. There is, however, a strong theoretical obstruction to the convergence of these methods (in dimension greater than 2). Finally we consider duopoly models that involve non-concave and non-coercive functionals. We study best reply maps and Nash equilibria in these models.
Author: Vincenzo Ancona Publisher: CRC Press ISBN: 9780203911143 Category : Mathematics Languages : en Pages : 390
Book Description
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
Author: PascalL.. Cherrier
Author: PascalL.. Cherrier
Author: Thierry Aubin
Author: Abdellah Hanani
Author: Raouf Chouikha
Author: Pascal Cherrier
Author: Thierry Aubin
Author: Sylvie Gillot
Author: Philippe Choné
Author: Vincenzo Ancona
Author: Université libre de Bruxelles. Centre d'études de recherche opérationnelle