Boundary conditions and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundaries

TL;DR

This paper studies boundary conditions for geometric Kramers-Fokker-Planck operators on manifolds with boundaries, establishing maximal accretivity, subelliptic estimates, and spectral properties relevant for applications like hypoelliptic Laplacians.

Contribution

Introduces a broad class of boundary conditions ensuring maximal accretivity and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundaries.

Findings

Boundary conditions ensuring maximal accretivity

Global subelliptic estimates established

Spectral and decay properties of the associated semigroup

Abstract

This article is concerned with maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic Laplacian.