Solvability in distributions for a class of singular differential operators. II
type: Item
instance of: scholarly article
title: Solvability in distributions for a class of singular differential operators. II
zbMATH Open document ID: 0708.35021
author: Hidetoshi Tahara
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: [For part I see ibid. 64, No.7, 219-222 (1988; Zbl 0693.35116).] Il s'agit de la continuation de la recherche du travail I prenant en considération le cas elliptique. Avec les notations du précédent travail, \(soit\) P\(=\sum_{j+| \alpha | \leq m}a_{j,\alpha}(t,x)(t\partial_ t)^ j\partial_ x^{\alpha}\), et en outre \(\sum_{j+| \alpha | =m}a_{j,\alpha}(0,0)\tau^ j\xi^{\alpha}\neq 0\), pour \((0,0)\neq (\tau,\xi)\in R_{\tau}\times R^ n_{\xi}.\) L'auteur démontre le théorème: Pour \(k\in (0,1,2,...)\) il y a un voisinage ouvert \(U_ k\) de (0,0) en \(R_ t\times R^ n_ x\), tel que pour chaque \(f(t,x)\in H^{-m-k}(U_ k)\) il y a une fonction \(u(t,x)\in H^{-m-2k-1}(U_ k)\cap H^{-k}_{loc}(U_ k(\pm))\), pour laquelle est \(Pu=f\) en \(U_ k\). [For part III see Publ. Res. Inst. Math. Sci. 26, No.1, 185-196 (1990; Zbl 0708.35022)].
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 35J30
zbMATH DE Number: 4163357
zbMATH Keywords: singular differential operators
reviewed by: Silvio Cinquini
MaRDI profile type: Publication
full work available at URL: pjaa.64.318
OpenAlex ID: W4245920086
cites work: Q3947998
cites work: Q4731515
cites work: Solvability in distributions for a class of singular differential operators. I
DOI: 10.3792/PJAA.64.318
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description: scientific article; zbMATH DE number 4163357