On the global solvability in Gevrey classes on the \(n\)-dimensional torus (Q1883366)
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scientific article; zbMATH DE number 2107214
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the global solvability in Gevrey classes on the \(n\)-dimensional torus |
scientific article; zbMATH DE number 2107214 |
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On the global solvability in Gevrey classes on the \(n\)-dimensional torus (English)
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12 October 2004
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The authors study global solvability in Gevrey classes on the \(n\)-dimensional torus \(\mathbb{T}^n\). A general necessary condition is first proved, similar to that in \textit{A. Corli} [Commun. Partial Differ. Equations 14, No. 1, 1--25 (1989; Zbl 0668.35002)] concerning the local case. Applications are then given to operators in \(\mathbb{T}^{n+1}\) of the form \[ P=- \partial^2_t- \biggl(\sum^n_{j=1} a_j(t)\,\partial_{x_j}\biggr)^2, \] where the functions \(a_j\) belong to \(G^s(\mathbb{T})\), \(s\geq 1\), and are real-valued.
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necessary condition
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