New PDF release: Equations Differentielles Operationnelles: Et Problèmes aux

By Dr. J. L. Lions (auth.)

ISBN-10: 3662237407

ISBN-13: 9783662237403

ISBN-10: 3662258390

ISBN-13: 9783662258392

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Extra info for Equations Differentielles Operationnelles: Et Problèmes aux Limites

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1. La condition necessaire et suffisante pour que soit un noyau ~ est obtenue dans ARONSZAJN-SMITH [5]. ° ~X,y 10. Problemes aux limites du type VISIK-SOBOLEV On donne dans ce No. quelques developpements sur les notes de VISIK-SOBOLEV [1J et LIONS [8J (des exposes un peu differents du suivant sont donnes dans MAGENES-STAMPACCHIA [1J et LIONS [1 bis]). On se place dans le cadre des No. 5 et 8. 2)', avec Re a (v, v) ~ oc IIv1l2, oc> 0, pour tout v E V. 2) Soient A et B deux espaces vectoriels topologiques localement convexes contenus (algebriquement et topologiquement) dans un meme espace localement convexe C.

Les eonditions aux limites, pour un meme espaee V, dependront de IX (sauf si V =H02 (Q), probleme de DIRICHLET). Les problemes de NEUMANN eorrespondront a V = H2 (Q). et Cas des systemes. Nous prenons maintenant pour H l'espaee produit V (Q)"; done t={A, ... }EH et (f, g) = tjEV(Q), SI • L (fi' gi)L'(Q)' i~l On eonsidere ensuite l'espaee produit avee ((u, v)) = • L ((Uj, Vj))Hmj(Q) ' i~l les mj >0 etant des entiers Si l'on pose quelconques. II• Ho"'i(Q) = ~m" ... , ... , m. , ... , ... ,mv(Q). , ...

1) A est un isomorphisme de D(A) sur H, soit ~ son inverse. fC'(H; D(A)) est, d'apres L. SCHWARTZ [3], [5], [6] (Theoreme des noyaux), d61ini par une distribution ~Xy et une seule, sur QxD; la distribution ~X,y est le noyau de GREEN du probleme aux limites correspondant. Si l'operateur A est un operateur differentiel hypo-elliptique (cf. No. 6), alors ~X,y est une fonction indetiniment differentiable en dehors de la diagonale (cf. 3). c'(Q) designant l'espace des distributions a support compact dans D 1.

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Equations Differentielles Operationnelles: Et Problèmes aux Limites by Dr. J. L. Lions (auth.)


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