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2020 Parametrix for a semiclassical subelliptic operator
Hart F. Smith
Anal. PDE 13(8): 2375-2398 (2020). 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.

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Hart F. Smith. "Parametrix for a semiclassical subelliptic operator." Anal. PDE 13 (8) 2375 - 2398, 2020. https://doi.org/10.2140/apde.2020.13.2375

Information

Received: 13 October 2018; Revised: 27 June 2019; Accepted: 25 September 2019; Published: 2020
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/apde.2020.13.2375

Subjects:
Primary: 35H20
Secondary: 35S05

Keywords: resonance , semiclassical analysis , subelliptic equations

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 8 • 2020
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