Comptes Rendus
Partial Differential Equations
The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators
[Le secteur d'analyticité de semi-groupes sous-markoviens non-symétriques engendrés par des opérateurs elliptiques]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 909-914.

We prove that a lower bound for the angle θp of the sector of analyticity of not necessarily symmetric submarkovian semigroups generated by second order elliptic operators in divergence form or by Ornstein–Uhlenbeck in Lμp is given by cotθp=(p2)2+p2(cotθ2)2/(2p1). If the semigroup is symmetric then we recover known results. In general, this lower bound is optimal.

Nous prouvons qu'une borne inférieure de l'angle θp du secteur d'analyticité de semi-groupes sous-markoviens non nécessairement symétriques qui sont engendrés par des opérateurs elliptiques sous forme divergencielle ou par des opérateurs de Ornstein–Uhlenbeck dans Lμp est donnée par la formule cotθp=(p2)2+p2(cotθ2)2/(2p1). Si le semi-groupe est symétrique on retrouve alors des résultats connus. En général, cette borne inférieure est optimale.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.04.003

Ralph Chill 1 ; Eva Fašangová 2 ; Giorgio Metafune 3 ; Diego Pallara 3

1 Université Paul-Verlaine – Metz, LMAM et CNRS, UMR 7122, bâtiment A, île du Saulcy, 57045 Metz cedex 1, France
2 Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
3 Dipartimento di Matematica “Ennio De Giorgi”, P.O.B. 193, 73100 Lecce, Italy
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Ralph Chill; Eva Fašangová; Giorgio Metafune; Diego Pallara. The sector of analyticity of nonsymmetric submarkovian semigroups generated by elliptic operators. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 909-914. doi : 10.1016/j.crma.2006.04.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.003/

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  • Ralph Chill; Hannes Meinlschmidt; Joachim Rehberg On the numerical range of second-order elliptic operators with mixed boundary conditions in Lp, Journal of Evolution Equations, Volume 21 (2021) no. 3, pp. 3267-3288 | DOI:10.1007/s00028-020-00642-6 | Zbl:1487.35201
  • D. Addona Analyticity of nonsymmetric Ornstein-Uhlenbeck semigroup with respect to a weighted Gaussian measure, Potential Analysis, Volume 54 (2021) no. 1, pp. 95-117 | DOI:10.1007/s11118-019-09819-2 | Zbl:7303856
  • Andrea Carbonaro; Oliver Dragičević Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients, Journal of the European Mathematical Society (JEMS), Volume 22 (2020) no. 10, pp. 3175-3221 | DOI:10.4171/jems/984 | Zbl:1458.35148

Cité par 3 documents. Sources : zbMATH

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