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Titolo:
Graphs between the elliptic and parabolic Harnack inequalities
Autore:
Delmotte, T;
Indirizzi:
Univ Toulouse 3, F-31062 Toulouse, France Univ Toulouse 3 Toulouse France F-31062 ouse 3, F-31062 Toulouse, France
Titolo Testata:
POTENTIAL ANALYSIS
fascicolo: 2, volume: 16, anno: 2002,
pagine: 151 - 168
SICI:
0926-2601(2002)16:2<151:GBTEAP>2.0.ZU;2-N
Fonte:
ISI
Lingua:
ENG
Soggetto:
RIEMANNIAN-MANIFOLDS; DIFFERENTIAL EQUATIONS; BROWNIAN-MOTION; RANDOM-WALK; KERNEL;
Keywords:
graph; Harnack inequality;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
30
Recensione:
Indirizzi per estratti:
Indirizzo: Delmotte, T Univ Toulouse 3, F-31062 Toulouse, France Univ Toulouse 3 Toulouse France F-31062 062 Toulouse, France
Citazione:
T. Delmotte, "Graphs between the elliptic and parabolic Harnack inequalities", POTENT ANAL, 16(2), 2002, pp. 151-168

Abstract

We present graphs that satisfy the uniform elliptic Harnack inequality, for harmonic functions, but not the stronger parabolic one, for solutions of the discrete heat equation. It is known that the parabolic Harnack inequality is equivalent to the conjunction of a volume regularity and a L-2 Poincare inequality. The first example of graph satisfying the elliptic but not the parabolic Harnack inequality is due to M. Barlow and R. Bass. It satisfies the volume regularity and not the Poincare inequality. We construct another example that does not satisfy the volume regularity.

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Documento generato il 19/01/20 alle ore 09:18:28