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Book Description
ON ETUDIE LE CARACTERE TRIVIAL DE LA SOLUTION DE CERTAINES EQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES DANS DES OUVERTS NON BORNES DE R**(N). ON CONSIDERE UNE NON LINEARITE DE F DU TYPE: F(U) OU= UF(U)/2 OU F(T)=SOM::(0)**(T)F(S)DS. DANS LA SECONDE PARTIE F EST TELLE QUE F(U) OU= 0
Book Description
ON ETUDIE LE CARACTERE TRIVIAL DE LA SOLUTION DE CERTAINES EQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES DANS DES OUVERTS NON BORNES DE R**(N). ON CONSIDERE UNE NON LINEARITE DE F DU TYPE: F(U) OU= UF(U)/2 OU F(T)=SOM::(0)**(T)F(S)DS. DANS LA SECONDE PARTIE F EST TELLE QUE F(U) OU= 0
Book Description
CE TRAVAIL TRAITE DEUX TYPES DE PROBLEMES. DANS LA PREMIERE PARTIE, ON ETUDIE L'INDICE D'OPERATEURS ELLIPTIQUES DU SECOND ORDRE A STRUCTURE DE DIVERGENCE, DANS L'ESPACE ENCLIDIEN DE DIMENSION N. LA DEUXIEME PARTIE TRAITE DE SOLUTIONS D'EQUATIONS ELLIPTIQUES NON LINEAIRES DANS DOMAINES NON BORNES. ON INTRODUIT LES ESPACES DE SOBOLEV A POIDS DANS LESQUELS ON RESOUD LES DEUX PROBLEMES
Author: J. Cea Publisher: Springer Science & Business Media ISBN: 1461224365 Category : Mathematics Languages : en Pages : 288
Book Description
Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for par tial differential equations with boundary conditions. He studied singulari ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph.D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before.
Book Description
NOUS SOUS-ENTENDONS PAR LE MOT PROBLEME, UN PROBLEME SEMI-LINEAIRE ELLIPTIQUE. NOUS COMMENCONS PAR MONTRER L'EXISTENCE, DANS LE PLAN, D'UNE SOLUTION ELEMENTAIRE PRINCIPALE POUR L'OPERATEUR SOMME DU LAPLACIEN ET D'UNE FONCTION C. NOUS MONTRONS ENSUITE, UN RESULTAT DE SYMETRIE RADIALE DES SOLUTIONS D'UN PROBLEME DANS LE PLAN. DANS LA TROISIEME PARTIE, NOUS MONTRONS DIFFERENTES ESTIMATIONS A PRIORI DES SOLUTIONS DE CERTAINS PROBLEMES. NOUS CONSIDERONS SUCCESSIVEMENT DES DOMAINES BORNES, EXTERIEURS ET LE PLAN TOUT ENTIER. LA QUATRIEME PARTIE TRAITE DE L'EXISTENCE D'UNE SOLUTION D'UN PROBLEME, DANS UN DOMAINE BORNE. LE DERNIER CHAPITRE PERMET DE MONTRER UN RESULTAT D'EXISTENCE DE SOLUTION POUR UN PROBLEME DANS LE PLAN. NOUS UTILISONS DES THEOREMES DE POINTS FIXES
Author: Jacques Louis Lions Publisher: Springer Science & Business Media ISBN: 3642651615 Category : Mathematics Languages : en Pages : 375
Book Description
1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
Author: Herve Le Dret Publisher: Springer Science & Business Media ISBN: 3642361757 Category : Mathematics Languages : fr Pages : 230
Book Description
Cet ouvrage est issu d’un cours de Master 2 enseigné à l’UPMC entre 2004 et 2007. Nous y présentons une sélection de techniques mathématiques orientées vers la résolution des équations aux dérivées partielles elliptiques semi-linéaires et quasi-linéaires. Après un vade-mecum d'analyse réelle et d'analyse fonctionnelle de base pour les EDP, sans démonstrations pour les points les plus connus, nous parcourons ainsi les théorèmes de point fixe classiques, les opérateurs de superposition dans les espaces de Lebesgue et de Sobolev, la méthode de Galerkin, les principes du maximum et la régularité elliptique, nous faisons une excursion assez longue dans divers aspects du calcul des variations puis terminons par les opérateurs monotones et pseudo-monotones. Tout ceci est agrémenté d’exemples et chaque chapitre est complété d'un nombre d’exercices qui croît essentiellement avec le numéro du chapitre, au fur et à mesure que de nouveaux matériaux sont présentés. This book stems from lectures notes of a Master 2 class held at UPMC between 2004 and 2007. A selection of mathematical techniques geared towards the resolution of semilinear and quasilinear elliptic partial differential equations is presented. After a short survival guide in basic real and functional analysis for PDEs, without proofs for the most well-known results, we walk through the classical fixed point theorems, the superposition operators in Lebesgue and Sobolev spaces, the Galerkin method, the maximum principles and elliptic regularity, we make a rather long foray into various aspects of the calculus of variations, and conclude with monotone and pseudo-monotone operators, by way of numerous examples. Each chapter is complemented by a number of exercises that grows with the chapter number as more and more material is made available.
Author: BRAHIM.. KHODJA
Author: BRAHIM.. KHODJA
Author: Boyan Sirakov
Author: Kamel Melouah
Author: J. Cea
Author: OULD AHMED.. ISSELKOU
Author: Miroslaw Krzyzanski
Author: European Environmental Mutagen Society
Author: A. Marino
Author: Jacques Louis Lions
Author: Herve Le Dret