0000000001289340

AUTHOR

Thierry Coulhon

showing 2 related works from this author

Gradient estimates for heat kernels and harmonic functions

2020

Let $(X,d,\mu)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carr\'e du champ". Assume that $(X,d,\mu,\E)$ supports a scale-invariant $L^2$-Poincar\'e inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\in (2,\infty]$: (i) $(G_p)$: $L^p$-estimate for the gradient of the associated heat semigroup; (ii) $(RH_p)$: $L^p$-reverse H\"older inequality for the gradients of harmonic functions; (iii) $(R_p)$: $L^p$-boundedness of the Riesz transform ($p<\infty$); (iv) $(GBE)$: a generalised Bakry-\'Emery condition. We show that, for $p\in (2,\infty)$, (i), (ii) (iii) are equivalent, wh…

Mathematics - Differential GeometryPure mathematicsPoincaré inequality01 natural sciencesMeasure (mathematics)Sobolev inequalitydifferentiaaligeometriaRiesz transformsymbols.namesakeMathematics - Analysis of PDEsMathematics - Metric GeometryLi-Yau estimates0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsRiesz transformosittaisdifferentiaaliyhtälötSemigroupDirichlet form010102 general mathematicsMetric Geometry (math.MG)harmoninen analyysiheat kernelsDifferential Geometry (math.DG)Harmonic functionMathematics - Classical Analysis and ODEssymbolspotentiaaliteoria010307 mathematical physicsIsoperimetric inequalityharmonic functionsAnalysisAnalysis of PDEs (math.AP)Journal of Functional Analysis
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Comité d'évaluation HCERES Unité BAGAP -Biodiversity, agroecology and landscape management under the supervision of the following Institutions and re…

2021

Under the decree No.2014-1365 dated 14 November 2014, 1 The president of Hcéres "countersigns the evaluation reports set up by the experts committees and signed by their chairman." (Article 8, paragraph 5); 2 The evaluation reports "are signed by the chairman of the experts committee". (Article 11, paragraph 2).

[SDV] Life Sciences [q-bio]
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