Inégalités de Gagliardo-Nirenberg pour les semi-groupes d'opérateurs et applications

Thierry Coulhon

doi:10.1007/BF00301787

Inégalités de Gagliardo-Nirenberg pour les semi-groupes d'opérateurs et applications

Thierry Coulhon

IP Paris

Research output: Contribution to journal › Article › peer-review

Abstract

One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L¹-L^∞ norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.

Original language	French
Pages (from-to)	343-353
Number of pages	11
Journal	Potential Analysis
Volume	1
Issue number	4
DOIs	https://doi.org/10.1007/BF00301787
Publication status	Published - 1 Dec 1992

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10.1007/BF00301787

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title = "In{\'e}galit{\'e}s de Gagliardo-Nirenberg pour les semi-groupes d'op{\'e}rateurs et applications",

abstract = "One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L1-L∞ norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.",

keywords = "Gagliardo-Nirenberg inequalities, Lipschitz spaces, Mathematics Subject Classifications (1991): 47D06, 58G11, 22E30, Nash inequalities, Sobolev inequalities, semigroups of operators, spectral gap",

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year = "1992",

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N2 - One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L1-L∞ norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.

AB - One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L1-L∞ norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.

KW - Gagliardo-Nirenberg inequalities

KW - Lipschitz spaces

KW - Mathematics Subject Classifications (1991): 47D06, 58G11, 22E30

KW - Nash inequalities

KW - Sobolev inequalities

KW - semigroups of operators

KW - spectral gap

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JO - Potential Analysis

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