Gaussian heat kernel bounds through elliptic Moser iteration
| العنوان: | Gaussian heat kernel bounds through elliptic Moser iteration |
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| المؤلفون: | Thierry Coulhon, Frédéric Bernicot, Dorothee Frey |
| المساهمون: | Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), Mathematical Sciences Institute (MSI), Australian National University (ANU), ANR-12-BS01-0013,HAB,Aux frontières de l'analyse Harmonique(2012), ANR-11-JS01-0001,AFoMEN,Analyse de Fourier Multilineaire et EDPs Nonlineaires(2011) |
| المصدر: | Journal de Mathématiques Pures et Appliquées Journal de Mathématiques Pures et Appliquées, Elsevier, 2016, 106 (6), pp.995-1037 |
| سنة النشر: | 2014 |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Pure mathematics, Hölder regularity of the heat semigroup, General Mathematics, gradient estimates, Characterization (mathematics), Space (mathematics), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Measure (mathematics), Riesz transform, Mathematics - Analysis of PDEs, 58J35, 42B20, 0103 physical sciences, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Direct proof, 0101 mathematics, Heat kernel, Mathematics, Heat kernel lower bounds, Semigroup, Applied Mathematics, Poincar e inequalities, 010102 general mathematics, Functional Analysis (math.FA), De Giorgi property, Mathematics - Functional Analysis, Differential Geometry (math.DG), Harmonic function, 58J35, 42B20, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], 010307 mathematical physics, Analysis of PDEs (math.AP) |
| الوصف: | On a doubling metric measure space endowed with a "carr\'e du champ", we consider $L^p$ estimates $(G_p)$ of the gradient of the heat semigroup and scale-invariant $L^p$ Poincar\'e inequalities $(P_p)$. We show that the combination of $(G_p)$ and $(P_p)$ for $p\ge 2$ always implies two-sided Gaussian heat kernel bounds. The case $p=2$ is a famous theorem of Saloff-Coste, of which we give a shorter proof, without parabolic Moser iteration. We also give a more direct proof of the main result in \cite{HS}. This relies in particular on a new notion of $L^p$ H\"older regularity for a semigroup and on a characterization of $(P_2)$ in terms of harmonic functions. Comment: v2: main result improved; slight reorganisation, title changed |
| اللغة: | English |
| تدمد: | 0021-7824 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f375da6a01645fd9ea7205ae36f704f5 http://arxiv.org/abs/1407.3906 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....f375da6a01645fd9ea7205ae36f704f5 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 00217824 |
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