Nonsolvability for differential operators with multiple complex characteristics
type: Item
instance of: scholarly article
title: Nonsolvability for differential operators with multiple complex characteristics
zbMATH Open document ID: 0798.35027
author: Todor Gramchev
published in: Journal of Mathematics of Kyoto University
publication date: 1994-06-08T00:00:00Z
review text: Let \(A\) be a classical analytic pseudodifferential operator of principal type modelled microlocally near a point by the Mizohata operator \(D_ n+ iy^ k_ n D_ 1\), \(k\in \mathbb{N}\). The main result is the local non- solvability of the operator \(P=A^ r+\) lower order terms, in the Gevrey classes \(G^ \sigma\) with \(1< \sigma\leq \infty\), where \(r\geq 2\), \(k\) is odd. Here \(G^ \infty= C^ \infty\). So the results of Cardoso, Treves, Popivanov and of Goldman are recovered. On the other hand, if \(k\) is even, the author finds the sufficient conditions for the operators to be solvable in \(G^ \sigma\) with \(1< \sigma< \sigma_ 0\), but not solvable if \(\sigma> \sigma_ 1\).
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 584578
zbMATH Keywords: Mizohata operator
zbMATH Keywords: local non-solvability
zbMATH Keywords: Gevrey classes
reviewed by: Yu V. Egorov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519125
OpenAlex ID: W1720339513
DOI: 10.1215/KJM/1250519125
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description: scientific article; zbMATH DE number 584578