Relations between different types of Hypoellipticity: A systematic approach

2025/05/17 by Victor, Bruno de Lessa, Ragognette, Luis F.
#35A09 (secondary) #35B65 #35H10 (primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.11801

Abstract

We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity implies another one and, in particular, when it can be extended for more general spaces. We also present a relation between certain types of hypoellipticity and local solvability (for the transpose) for a family of operators.

Citations

• Regularity and solvability of linear differential operators in Gevrey spaces: omitted proofs
• Subelliptic Estimates
• Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential
• Intermediate Optimal Gevrey Exponents Occur

Related

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• Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus
• On Analytic Solvability and Hypoellipticity For \dbar and \dbar_b
• On partially hypoelliptic operators. Part II: Pseudo differential operators
• On uniformity for the polar to partially hypoelliptic operators