Sur une inegalite de type Poincare

Fabrice Planchon

Description

Niveau: Supérieur, Licence, Bac+2
Sur une inegalite de type Poincare Fabrice Planchon ? Resume. On demontre que pour une fonction f dont le spectre frequenciel est disjoint de la boule unite, ?|f |q?1?Lq? . ??(|f |q?1)?Lq? , pour q ≥ 2. Pour q = 2 ceci n'est que l'inegalite de Poincare, et en utilisant Holder on peut obtenir ?|f |q/2?L2 . ??(|f |q/2)?L2 , qui a d'interessantes applications pour les equations aux derivees partielles. Abstract. Let f be such that its Fourier transform is supported outside the unit ball. We prove the following inequality ?|f |q?1?Lq? . ??(|f |q?1)?Lq? , for q ≥ 2. For q = 2 this is nothing but Poincare inequality, while by using Holder we get ?|f |q/2?L2 . ??(|f |q/2)?L2 , which has interesting applications for partial differen- tial equations. Introduction Considerons une fonction f qu'on prendra dans la classe de Schwartz, dont le support de la transformee de Fourier est compact et ne contient pas zero. Les theoremes classiques de multiplicateur de Fourier nous assurent alors que controler f ou ?f est equivalent dans tous les espaces de Lebesgue Lp. Considerons maintenant ? ≥ ? > 1, q = ? + ? > 2 : par application successive de l'inegalite de Holder et de l'inegalite de Bernstein, il vient ∫ |?f |?|f |? .

• interessantes applications pour les equations aux derivees partielles


• norme besov consideree


• evo- lution des solutions des equations de navier-stokes incompressibles


• theoreme de multiplicateurs de fourier


• application naturelle


• espaces de lebesgue lp

Sujets

• Planchon

Informations

• Publié par: profil-vieg-2012
• Nombre de lectures: 65

Extrait

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