Parametrix for a semiclassical subelliptic operator

Smith, Hart F.

doi:10.2140/apde.2020.13.2375

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Parametrix for a semiclassical subelliptic operator

Hart F. Smith

Vol. 13 (2020), No. 8, 2375–2398

DOI: 10.2140/apde.2020.13.2375

Abstract

We demonstrate a parametrix construction, together with associated pseudodifferential operator calculus, for an operator of sum-of-squares type with semiclassical parameter. The form of operator we consider includes the generator of kinetic Brownian motion on the cosphere bundle of a Riemannian manifold. Regularity estimates in semiclassical Sobolev spaces are proven by establishing mapping properties for the parametrix.

Keywords

subelliptic equations, semiclassical analysis, resonance

Mathematical Subject Classification 2010

Primary: 35H20

Secondary: 35S05

Milestones

Received: 13 October 2018

Revised: 27 June 2019

Accepted: 25 September 2019

Published: 28 December 2020

Authors

Hart F. Smith
Department of Mathematics University of Washington Seattle, WA United States

Vol. 13, No. 8, 2020