Nash type Inequalities and

Patrick Maheux

Description

Nash-type Inequalities and decay of semigroups. Patrick Maheux University of Orleans. Federation Denis Poisson. Workshop in Nanterre . June 4-5-6, 2007.

• finite measure


• let ?


• ∂tt ∂t


• poincare inequality


• dimension can


• ?f ?


• infinitesimal generator

Sujets

• Poisson
• Nanterre
• Maheux
• ?-finite measure
• Poincaré inequality
• Infinitesimal generator

Informations

• Publié par: pefav
• Nombre de lectures: 32
• Langue: English

Extrait

Nash-type Inequalities and

decay of semigroups.

Patrick Maheux UniversityofOrl´eans. F´ed´erationDenisPoisson .

Workshop in Nanterre . June 4-5-6,

2007.

SETTING

• ( X, µ ) measure space with µ a σ -finite measure.

• ( T t ) t> 0 : a symmetric submarkovian semi- group:

• ( T t f,h ) = ( f, T t h ) , ∀ f,g ∈ L 2

• ∀ f ∈ L 2 , 0 ≤ f ≤ 1 ⇒ 0 ≤ T t f ≤ 1 • ( T t ) t> 0 acts as a contraction on L p .

• L : infinitesimal generator associated to the semigroup T t = e − t L

t = T ∂ ∂ T t − A t f

• E : Dirichlet form associated to ( T t ) :

E ( f ) = ( L f,f ) , f ∈ D ( L )

Important property

∀ f ∈ D ( E ) ⇒ h = ( f ∨ 0) ∧ 1 ∈ D ( E )

and

E ( h ) ≤ E ( f )