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EnglishIf L = \sum_{j=1}X_j^2 + X_0 is a Hormander partial differential operator in R^N, we give sufficient conditions on the X_j's for the existence of a Lie group structure G = (R^N,*), not necessarily nilpotent, such that L is left invariant on G. We also investigate the existence of a global fundamental solution Gamma for L, providing results ensuring a suitable left invariance property of. Examples are given for operators L to which our results apply: some are new, some appear in recent literature, usually quoted as Kolmogorov-Fokker-Planck type operators.
| Titolo: | Lie groups related to Hörmander operators and Kolmogorov-Fokker-Planck equations |
| Autore/i: | BONFIGLIOLI, ANDREA; LANCONELLI, ERMANNO |
| Autore/i Unibo: | |
| Anno: | 2012 |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.3934/cpaa.2012.11.1587 |
| Abstract: | If L = \sum_{j=1}X_j^2 + X_0 is a Hormander partial differential operator in R^N, we give sufficient conditions on the X_j's for the existence of a Lie group structure G = (R^N,*), not necessarily nilpotent, such that L is left invariant on G. We also investigate the existence of a global fundamental solution Gamma for L, providing results ensuring a suitable left invariance property of. Examples are given for operators L to which our results apply: some are new, some appear in recent literature, usually quoted as Kolmogorov-Fokker-Planck type operators. |
| Data prodotto definitivo in UGOV: | 2013-05-23 17:54:50 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/11585/92666
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