Geodesic
Localizations of partial differential operators and surjectivity on real analytic functions
Studia Mathematica, Tome 140 (2000) no. 1, pp. 15-40

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DOI

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 ⊂ ℝ^n$. 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 $P_{m,Θ}$ of the principal part $P_m$ is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for $P_{m,Θ}$. Under additional assumptions $P_m$ must be locally hyperbolic.
DOI : 10.4064/sm-140-1-15-40
Keywords: partial differential operator, real analytic function, elementary solution, hyperbolicity, local hyperbolicity 
Michael Langenbruch. Localizations of partial differential operators and surjectivity on real analytic functions. Studia Mathematica, Tome 140 (2000) no. 1, pp. 15-40. doi: 10.4064/sm-140-1-15-40
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