Gevrey local solvability in locally integrable structures

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• 作者：Francesco Malaspina (1)
  Fabio Nicola (1)
  
• 关键词：Gevrey local solvability ; Locally integrable structures ; Poincar茅 lemma ; Differential complexes ; Involutive structures ; 35S30 ; 47G30 ; 42C15
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：193
• 期：5
• 页码：1491-1502
• 全文大小：188 KB
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• 作者单位：Francesco Malaspina (1)
  Fabio Nicola (1)
  
  1. Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
  
• ISSN：1618-1891

文摘

We consider a locally integrable real-analytic structure, and we investigate the local solvability in the category of Gevrey functions and ultradistributions of the complex \(\mathrm{d}^{\prime }\) naturally induced by the de Rham complex. We prove that the so-called condition \(Y(q)\) on the signature of the Levi form, for local solvability of \(\mathrm{d}^{\prime }u=f\) , is still necessary even if we take \(f\) in the classes of Gevrey functions and look for solutions \(u\) in the corresponding spaces of ultradistributions.