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Analytic approximation for homogeneous solutions of linear PDE’s. (English) Zbl 0531.35017

Journ. Équ. Dériv. Partielles, Saint-Jean-De-Monts 1983, Exp. No. 1, 4 p. (1983).
Let P(x,D) be a differential operator with analytic coefficients in an open set in \(R^ n\) for which the principal symbol of P is nowhere identically zero. Two partial answers to the question of when are distribution solutions of \(P(x,D)u=0\) locally the limit of real analytic solutions to this equation are stated, namely, when P has simple (complex) characteristics and when P is a left invariant operator defined on a general Lie group. For proofs, see e.g., the author and F. Trèves, Duke Math. J. 50, 285-301 (1983).
Reviewer: P.W.Schaefer

MSC:

35G05 Linear higher-order PDEs
35A35 Theoretical approximation in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)