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ArticleOriginal scientific text

Title

Localizations of partial differential operators and surjectivity on real analytic functions

Authors 1

Affiliations

  1. Department of Mathematics, University of Oldenburg, D-26111 Oldenburg, Germany

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 an open set Ω⊂ℝn. Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization Pm,Θ of the principal part Pm is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for Pm,Θ. Under additional assumptions Pm must be locally hyperbolic.

Keywords

ENG
partial differential operator, real analytic function, elementary solution, hyperbolicity, local hyperbolicity

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Studia Mathematica
2000/140/1
Export to PBN, Opens in new tab
Pages:
15-40
Main language of publication
English
Received
1999-02-01
Accepted
1999-12-13
Published
2000
Exact and natural sciences