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Introduction: the Euclidean case Approximation by a discrete operator

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36 pages
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


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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
emmanuel.russ@univ-cezanne.fr
elliptic
Emmanuel Russ
form:
order
Consider second
emmanuel.russ@univ-cezanne.fr
div(Ar)
=
L
elliptic operators in divergence
L
be
can
What ?
and parabolic regularity theory for
RehA(x)ξ, ξi
said about
the elliptic
Cn.
n R,for allξ
δ|ξ|2
|hA(x)ξ, ηi|
a.e.x
a.e.xRn,for allξ, η
whereA:RnMn(C) i.e., for someδ >0,
δ1|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 etL.
regularity
is
u+Lu t
related to
Emmanuel Russ
=
the
the
of
f.
solutions
the
of
solutions
properties
of
the
emmanuel.russ@univ-cezanne.fr
of
semigroup