Semiclassical analysis of a nonlinear eigenvalue problem and non analytic hypoellipticity

2003/04/15 by Bernard Helffer, Helffer, Bernard, Didier Robert +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.math/0304201

arxiv created 2003/04/15 · openalex publication_date 2003/04/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity and obtain a general family of hypoelliptic, but not analytic hypoelliptic operators.

Related

• Non-Linear Eigenvalues and Analytic Hypoellipticity
• Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics
• Failure of analytic hypoellipticity in a class of PDOs
• Non linear eigenvalue problems
• Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical\n operators with double characteristics