Introduction: the Euclidean case Approximation by a discrete operator

Emmanuel Russ

Description

Introduction: the Euclidean case Approximation by a discrete operator Elliptic and parabolic regularity on graphs Estimates for the square root of L Elliptic and parabolic regularity for discrete elliptic operators on graphs Emmanuel Russ Université Paul Cézanne Aix-Marseille III LATP Joint with Nadine Badr, Université Paris XI CIRM, 25-28/03/2008 Emmanuel Russ

• order elliptic


• parabolic regularity theory


• iff there exist


• semigroup e?tl


• gaussian property


• contraction semigroup


• elliptic regularity


• parabolic regularity

Sujets

• Cezanne
• Université Paris-Sud 11
• Quasicontraction semigroup
• Hypoelliptic operator

Informations

• Publié par: pefav
• Publié le: 01 mars 2008
• Nombre de lectures: 17
• Langue: English

Extrait

Elliptic

Introduction: the Euclidean case Approximation by a discrete operator Elliptic and parabolic regularity on graphs Estimates for the square root ofL

and

regularity for discrete ors on graphs

parabolic operat

Emmanuel

Russ

Université Paul Cézanne Aix-Marseille III LATP

Joint with Nadine Badr, Université Paris XI

CIRM,

25-28/03/2008

Emmanuel Russ

[e-mail]

elliptic

Emmanuel Russ

form:

order

Consider second

[e-mail]

−div(Ar)

=

L

elliptic operators in divergence

L

be

can

What ?

and parabolic regularity theory for

RehA(x)ξ, ξi

said about

the elliptic

∈C n .

n R,for allξ

≥

δ|ξ| 2

|hA(x)ξ, ηi|

≤

∈

a.e.x

a.e.x∈R n ,for allξ, η

whereA:R n →M n (C) i.e., for someδ >0,

δ −1 |ξ| |η|

n ∈C,

and

is measurable, bounded

elliptic,

uniformly

case

I.

Introduction: the Euclidean case Approximation by a discrete operator Elliptic and parabolic regularity on graphs Estimates for the square root ofL Introduction: the Euclidean

By

elliptic

Introduction: the Euclidean case Approximation by a discrete operator Elliptic and parabolic regularity on graphs Estimates for the square root ofL

regularity

assuming some

By

parabolic

,

we

regularity

mean

on

f.

regularity

Lu

=f

of

regularity, we mean regularity

This parabolic e −tL .

regularity

is

∂ ∂ u +Lu t

related to

Emmanuel Russ

=

the

the

of

f.

solutions

the

of

solutions

properties

of

the

[e-mail]

of

semigroup