Singularities of Hypoelliptic Green Functions

Gérard Ben Arous (1) , Mihai Gradinaru (2)

1 IMA - Institut de Mathématiques
2 IECN - Institut Élie Cartan de Nancy

This paper is devoted to a precise description of the singularity near the diagonal of the Green function associated to a hypoelliptic operator using a probabilistic approach. Examples and some applications to potential theory are given.

Mots clés: degenerate diffusion; Taylor stochastic expansion; capacity; Hypoelliptic operator; Green function

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Gérard Ben Arous, Mihai Gradinaru. Singularities of Hypoelliptic Green Functions. Potential Analysis, 1998, 8, pp.217-258. ⟨10.1023/A:1008608825872⟩. ⟨hal-00120169⟩