Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions

Bogachev V, Röckner M, Wang F-Y (2001)
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332(4): 333-338.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch , Französisch
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Abstract / Bemerkung
We obtain sufficient conditions in terms of Lyapunov functions for the existence of invariant measures for diffusions on finite dimensional manifolds and prove some global regularity results for such measures. These results are extended to countable products of finite dimensional manifolds. A new concept of weak elliptic equations for measures on infinite dimensional manifolds is introduced. As an application we obtain some a priori estimates for Gibbs measures on countable products of manifolds and prove a new existence result for such measures. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
Erscheinungsjahr
Zeitschriftentitel
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
Band
332
Ausgabe
4
Seite(n)
333-338
ISSN
PUB-ID

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Bogachev V, Röckner M, Wang F-Y. Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. 2001;332(4):333-338.
Bogachev, V., Röckner, M., & Wang, F. - Y. (2001). Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 332(4), 333-338. doi:10.1016/S0764-4442(01)01836-5
Bogachev, V., Röckner, M., and Wang, F. - Y. (2001). Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332, 333-338.
Bogachev, V., Röckner, M., & Wang, F.-Y., 2001. Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 332(4), p 333-338.
V. Bogachev, M. Röckner, and F.-Y. Wang, “Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, vol. 332, 2001, pp. 333-338.
Bogachev, V., Röckner, M., Wang, F.-Y.: Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics. 332, 333-338 (2001).
Bogachev, Vladimir, Röckner, Michael, and Wang, Feng-Yu. “Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions”. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332.4 (2001): 333-338.