Around Nash inequalities

Bakry, Dominique; Bolley, François; Gentil, Ivan

doi:10.5802/jedp.59

Bakry, Dominique ¹ ; Bolley, François ² ; Gentil, Ivan ³

¹ Institut de Mathématiques de Toulouse, UMR CNRS 5219, Institut Universitaire de France, Université de Toulouse, Route de Narbonne, 31062 Toulouse - France
² Ceremade, UMR CNRS 7534, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75016 Paris - France
³ Institut Camille Jordan, UMR CNRS 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex - France

Journées équations aux dérivées partielles (2010), article no. 2, 16 p.

DOI : 10.5802/jedp.59

Affiliations des auteurs :

Bakry, Dominique ¹ ; Bolley, François ² ; Gentil, Ivan ³

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     doi = {10.5802/jedp.59},
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Bakry, Dominique; Bolley, François; Gentil, Ivan. Around Nash inequalities. Journées équations aux dérivées partielles (2010), article  no. 2, 16 p. doi : 10.5802/jedp.59. http://www.numdam.org/articles/10.5802/jedp.59/

Bibliographie
Cité par

[1] Bakry, D. L’hypercontractivité et son utilisation en théorie des semigroupes, Lectures on probability theory (Saint-Flour, 1992) (Lecture Notes in Math. 1581), Springer, Berlin, 1994, pp. 1-114 | MR | Zbl

[2] Bakry, D.; Bolley, F.; Gentil, I.; Maheux, P. Weighted Nash inequalities, Preprint

[3] Bakry, D.; Coulhon, T.; Ledoux, M.; Saloff-Coste, L. Sobolev inequalities in disguise, Indiana Univ. Math. J., Volume 44 (1995) no. 4, pp. 1033-1074 | DOI | MR | Zbl

[4] Bakry, D.; Ledoux, M. Sobolev inequalities and Myers’s diameter theorem for an abstract Markov generator, Duke Math. J., Volume 85 (1996) no. 1, pp. 253-270 | DOI | MR | Zbl

[5] Bendikov, A.; Coulhon, T.; Saloff-Coste, L. Ultracontractivity and embedding into $L^{\infty}$ , Math. Ann., Volume 337 (2007) no. 4, pp. 817-853 | MR | Zbl

[6] Carlen, E. A.; Loss, M. Sharp constant in Nash’s inequality, Internat. Math. Res. Notices, Volume 7 (1993), pp. 213-215 | DOI | MR | Zbl

[7] Davies, E. B. Heat kernels and spectral theory, Cambridge Tracts in Mathematics, 92, Cambridge University Press, Cambridge, 1990 | MR | Zbl

[8] Gross, L. Logarithmic Sobolev inequalities, Amer. J. Math., Volume 97 (1975) no. 4, pp. 1061-1083 | MR | Zbl

[9] Nash, J. Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., Volume 80 (1958), pp. 931-954 | MR | Zbl

[10] Nelson, E. The free Markoff field, J. Functional Analysis, Volume 12 (1973), pp. 211-227 | MR | Zbl

[11] Varopoulos, N. Th. Hardy-Littlewood theory for semigroups, J. Funct. Anal., Volume 63 (1985) no. 2, pp. 240-260 | DOI | MR | Zbl

[12] Wang, F.-Y. Functional inequalities for empty essential spectrum, J. Funct. Anal., Volume 170 (2000) no. 1, pp. 219-245 | DOI | MR | Zbl

[13] Wang, F.-Y. Functional inequalities and spectrum estimates: the infinite measure case, J. Funct. Anal., Volume 194 (2002) no. 2, pp. 288-310 | MR | Zbl

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