Vol. 13, No. 8, 2020
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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