Gaussian type bounds for the Neumann-Green function of a general parabolic operator

Mourad Choulli (1) , Laurent Kayser (2)

1 EDP - Equations aux dérivées partielles
2 IECL - Institut Élie Cartan de Lorraine

Based on the fact that the Neumann-Green function can be constructed as a perturbation of the fundamental solution by a single-layer potential, we establish a gaussian lower bound and a gaussian type upper bound for the Neumann-Green function for a general parabolic operator. We build our analysis on old tools coming from the construction of a fundamental solution of a general parabolic operator by means of the so-called parametrix method. At the same time we provide a simple proof for the gaussian two-sided bounds for the fundamental solution.

Mots clés: parabolic operator; fundamental solution; Neumann-Green function; parametrix; heat kernel.; heat kernel

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Laurent Kayser. Gaussian type bounds for the Neumann-Green function of a general parabolic operator. 2013. ⟨hal-00773492v2⟩