Gevrey semiglobal solvability for a class of elliptic vector fields with degeneracies

Gabriel Araújo, Adalberto P. Bergamasco and Paulo L. Dattori da Silva

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3153-3172

Abstract: We deal with Gevrey solvability of a class of complex vector fields defined on Ω=R×S1$\Omega = \mathbb {R}\times S^1$, given by L=∂/∂t+(a(x,t)+ib(x,t))∂/∂x$\mathcal {L} = \partial /\partial t+(a(x,t)+ib(x,t))\partial /\partial x$, b≢0$b\not\equiv 0$, near the characteristic set Σ={0}×S1$\Sigma = \lbrace 0\rbrace \times S^1$. Diophantine conditions appear in a natural way in our results.

Date: 2023
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