Around Nash inequalities

Dominique Bakry[1]; François Bolley[2]; Ivan Gentil[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)

  • page 1-16
  • ISSN: 0752-0360

How to cite

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Bakry, Dominique, Bolley, François, and Gentil, Ivan. "Around Nash inequalities." Journées Équations aux dérivées partielles (2010): 1-16. <http://eudml.org/doc/116383>.

@article{Bakry2010,
affiliation = {Institut de Mathématiques de Toulouse, UMR CNRS 5219, Institut Universitaire de France, Université de Toulouse, Route de Narbonne, 31062 Toulouse - France; Ceremade, UMR CNRS 7534, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75016 Paris - France; Institut Camille Jordan, UMR CNRS 5208, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex - France},
author = {Bakry, Dominique, Bolley, François, Gentil, Ivan},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
month = {6},
pages = {1-16},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Around Nash inequalities},
url = {http://eudml.org/doc/116383},
year = {2010},
}

TY - JOUR
AU - Bakry, Dominique
AU - Bolley, François
AU - Gentil, Ivan
TI - Around Nash inequalities
JO - Journées Équations aux dérivées partielles
DA - 2010/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 16
LA - eng
UR - http://eudml.org/doc/116383
ER -

References

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  1. D. Bakry, L’hypercontractivité et son utilisation en théorie des semigroupes, Lectures on probability theory (Saint-Flour, 1992) (1994), 1-114, Springer, Berlin Zbl0856.47026MR1307413
  2. D. Bakry, F. Bolley, I. Gentil, P. Maheux, Weighted Nash inequalities, Preprint 
  3. D. Bakry, T. Coulhon, M. Ledoux, L. Saloff-Coste, Sobolev inequalities in disguise, Indiana Univ. Math. J. 44 (1995), 1033-1074 Zbl0857.26006MR1386760
  4. D. Bakry, M. Ledoux, Sobolev inequalities and Myers’s diameter theorem for an abstract Markov generator, Duke Math. J. 85 (1996), 253-270 Zbl0870.60071MR1412446
  5. A. Bendikov, T. Coulhon, L. Saloff-Coste, Ultracontractivity and embedding into L ∞ , Math. Ann. 337 (2007), 817-853 Zbl1132.47031MR2285739
  6. E. A. Carlen, M. Loss, Sharp constant in Nash’s inequality, Internat. Math. Res. Notices 7 (1993), 213-215 Zbl0822.35018MR1230297
  7. E. B. Davies, Heat kernels and spectral theory, 92 (1990), Cambridge University Press, Cambridge Zbl0699.35006MR1103113
  8. L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083 Zbl0318.46049MR420249
  9. J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954 Zbl0096.06902MR100158
  10. E. Nelson, The free Markoff field, J. Functional Analysis 12 (1973), 211-227 Zbl0273.60079MR343816
  11. N. Th. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260 Zbl0608.47047MR803094
  12. F.-Y. Wang, Functional inequalities for empty essential spectrum, J. Funct. Anal. 170 (2000), 219-245 Zbl0946.58010MR1736202
  13. F.-Y. Wang, Functional inequalities and spectrum estimates: the infinite measure case, J. Funct. Anal. 194 (2002), 288-310 Zbl1021.58007MR1934605

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