manuscripta mathematica

, Volume 103, Issue 2, pp 241–263

Surjective partial differential operators on real analytic functions defined on open convex sets

  • M. Langenbruch

DOI: 10.1007/PL00005858

Cite this article as:
Langenbruch, M. manuscripta math. (2000) 103: 241. doi:10.1007/PL00005858

Abstract:

Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on a covex open set Ω⊂ℝn. Let L(Pm) denote the localizations at ∞ (in the sense of Hörmander) of the principal part Pm. Then Q(x+iτN)≠ 0 for (x,τ)∈ℝn×(ℝ\{ 0}) for any QL(Pm) if N is a normal to δΩ which is noncharacteristic for Q. Under additional assumptions this implies that Pm must be locally hyperbolic.

Mathematics Subject Classification (2000): 35E20, 35E05, 35A18, 35A21 

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • M. Langenbruch
    • 1
  1. 1.University of Oldenburg, Department of Mathematics, 26111 Oldenburg, Germany e-mail: langenbruch@mathematik.uni-oldenburg.deDE

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