Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions |
| |
| Institution: | 1. Moscow State University, 119899 Moscow, Russia;2. Fakultät für Mathematik, Universität Bielefeld, D-33615 Bielefeld, Germany;3. Department of Mathematics, Beijing Normal University, Beijing 100875, China;1. Department of Biology, University of the Azores, 9501-801, Ponta Delgada, Portugal;2. cE3c, Centre for Ecology, Evolution and Environmental Changes, and Azorean Biodiversity Group, University of the Azores, 9501-801, Ponta Delgada, Portugal;3. CVARG, Center of Volcanology and Geological Risks Assessment, University of the Azores, 9501-801, Ponta Delgada, Portugal;3. Institute for Pharmacology, Center for Physiology and Pharmacology, Medical University of Vienna, Währinger Str. 13a, 1090 Vienna, Austria;4. Institut Interdisciplinaire de Neurosciences, CNRS UMR 5297, Université Bordeaux 2, 146 rue Léo Saignat, 33077 Bordeaux, France |
| |
| Abstract: | 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. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
