Global analytic hypoellipticity and solvability of certain operators subject to group actions

2021/11/13 by Araújo, Gabriel, Ferra, Igor A., Ragognette, Luis F. · 2 citations
#35A01 #35H10 (primary) #35R01 #35R03 (secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.07165

Abstract

On T × G, where T is a compact real-analytic manifold and G is a compact Lie group, we consider differential operators P which are invariant by left translations on G and are elliptic in T. Under a mild technical condition, we prove that global hypoellipticity of P implies its global analytic-hypoellipticity (actually Gevrey of any order s ≥ 1). We also study the connection between the latter property and the notion of global analytic (resp. Gevrey) solvability, but in a much more general setup.

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• Global Solvability for Involutive Systems on Non-Compact Manifolds
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