Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds

Röckner M, Wang F-Y (2003)
Forum Mathematicum 15(6): 893-921.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Wang, Feng-Yu
Abstract / Bemerkung
Under a curvature condition, we obtain some criteria of supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on Riemannian manifolds. As consequences, some sufficient and necessary conditions are presented for these two contraction properties. Then, based on a perturbation argument, ultracontractivity is studied for symmetric diffusions with non-smooth drifts. Moreover, we provide a way to study contraction properties using isoperimetric inequalities. To illustrate the main results, some typical examples are constructed, where one of them shows that supercontractivity is strictly weaker than ultracontractivity as already known in the flat case.
Erscheinungsjahr
2003
Zeitschriftentitel
Forum Mathematicum
Band
15
Ausgabe
6
Seite(n)
893-921
ISSN
0933-7741
Page URI
https://pub.uni-bielefeld.de/record/1609893

Zitieren

Röckner M, Wang F-Y. Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds. Forum Mathematicum. 2003;15(6):893-921.
Röckner, M., & Wang, F. - Y. (2003). Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds. Forum Mathematicum, 15(6), 893-921. https://doi.org/10.1515/form.2003.044
Röckner, M., and Wang, F. - Y. (2003). Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds. Forum Mathematicum 15, 893-921.
Röckner, M., & Wang, F.-Y., 2003. Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds. Forum Mathematicum, 15(6), p 893-921.
M. Röckner and F.-Y. Wang, “Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds”, Forum Mathematicum, vol. 15, 2003, pp. 893-921.
Röckner, M., Wang, F.-Y.: Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds. Forum Mathematicum. 15, 893-921 (2003).
Röckner, Michael, and Wang, Feng-Yu. “Supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on manifolds”. Forum Mathematicum 15.6 (2003): 893-921.

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