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Potential Analysis

, Volume 38, Issue 3, pp 1001–1030 | Cite as

A Poincaré Cone Condition in the Poincaré Group

  • Camille TardifEmail author
Article
  • 86 Downloads

Abstract

Ben Arous and Gradinaru (Potential Anal 8(3):217–258, 1998) described the singularity of the Green function of a general sub-elliptic diffusion. In this article we first adapt their proof to the more general context of a hypoelliptic diffusion. In a second time, we deduce a Wiener criterion and a Poincaré cone condition for a relativistic diffusion with values in the Poincaré group (i.e the group of affine direct isometries of the Minkowski space-time).

Keywords

Green function Wiener test Poincaré cone condition Relativistic diffusion Hypoelliptic operator 

Mathematics Subject Classifications (2010)

58J65 60J60 35H05 60H10 60J45 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeUniversité de StrasbourgStrasbourgFrance

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