Invariants and spaces of zero solutions of linear partial differential operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Invariants and spaces of zero solutions of linear partial differential operators

Authors:	Dietmar Vogt

Institution:	1. FB Math.-Nat., Bergische Universit?t Wuppertal, Gauss-Strasse 20, D-42097, Wuppertal, Germany

Abstract:	It is shown that for open convex $\Omega \, \subset \,{\user2{\mathbb{R}}}^{d}$ , d > 1 and a nontrivial polynomial P the space ${\user1{\mathcal{N}}}_{p} (\Omega )\, = \,{\left\{ {f\, \in \,C^{\infty } (\Omega )\,:\,P(D)f\, = \,0} \right\}}$ does not have property $(\overline{\overline \Omega})$ . If P is elliptic or homogeneous, then this holds for every open Ω. For $\Omega \, = \,{\user2{\mathbb{R}}}^{d}$ even $(\overline{\Omega})$ cannot occur and if it occurs for some Ω, then P must be hypoelliptic. Received: 18 July 2005

Keywords:	Primary 46A63 35E20 Secondary 35G30 46A04 46E10 46M18
本文献已被 SpringerLink 等数据库收录！