Global solvability for first order real linear partial differential operators II

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• 作者：José ; R. dos Santos Filho^a ; ^{santos@dm.ufscar.br} ; Maurí ; cio Fronza da Silva^b ; ^{mfronza@smail.ufsm.br}
• 关键词：35A05 ; 35F05
• 刊名：Journal of Differential Equations
• 出版年：2012
• 出版时间：1 August, 2012
• 年：2012
• 卷：253
• 期：3
• 页码：933-950
• 全文大小：233 K

文摘

Let L be a real vector field on a smooth manifold X, vanishing at exactly one point . From the pioneering work of B. Malgrange (1955-1956) , we know that solvability of on , for , implies that: (a) X is L-convex. Also, it follows: (b) a non-resonance condition for the jet-solvability at .

In a previous paper, in addition to (a) and (b), the authors showed that P is globally solvable on if we assume: (c) a non-resonance condition in order to linearize L near ; that (d) the only relatively compact orbit of L is ; and that (e) c is real.

Here we obtain the same conclusion without (c) and (e).