If L is a Hormander partial differential operator in R^N, we give sufficient conditions 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 ¡ 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. Non trivial examples of homogeneous groups are also given.

On left-invariant Hormander operators in R^N: applications to the Kolmogorov-Fokker-Planck equations (Russian Version) / A. Bonfiglioli; E. Lanconelli. - In: SOVREMENNAÂ MATEMATIKA. FUNDAMENTALʹNYE NAPRAVLENIÂ. - ISSN 2413-3639. - STAMPA. - 36:(2010), pp. 24-35.

On left-invariant Hormander operators in R^N: applications to the Kolmogorov-Fokker-Planck equations (Russian Version)

BONFIGLIOLI, ANDREA;LANCONELLI, ERMANNO
2010

Abstract

If L is a Hormander partial differential operator in R^N, we give sufficient conditions 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 ¡ 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. Non trivial examples of homogeneous groups are also given.
2010
On left-invariant Hormander operators in R^N: applications to the Kolmogorov-Fokker-Planck equations (Russian Version) / A. Bonfiglioli; E. Lanconelli. - In: SOVREMENNAÂ MATEMATIKA. FUNDAMENTALʹNYE NAPRAVLENIÂ. - ISSN 2413-3639. - STAMPA. - 36:(2010), pp. 24-35.
A. Bonfiglioli; E. Lanconelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/110489
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