Microfunctions for boundary value problems. (English) Zbl 0715.58037

Algebraic analysis, Pap. Dedicated to Prof. Mikio Sato on the Occas. of his Sixtieth Birthday, Vol. 2, 809-819 (1989).
[For the entire collection see Zbl 0665.00008.]
The author refines the theory of microfunctions at the boundary introduced in his previous paper [Sémin., Equations Dériv. Partielles 1985-1986, Exposé No.13, 12 p. (1986; Zbl 0638.58027)]. In particular he describes functorially a “boundary value” morphism from an open set \(\Omega\) to \(N=\partial \Omega\), which coincides with the classical “trace morphism” for solutions of non-characteristic systems. He also shows that the microsupport of traces on N coincides with the projection along the bicharacteristic leaves of \(N^{{\mathbb{C}}}\) of the microsupport at the boundary. Finally he recovers in his joint theory with M. Kashiwara of abstract microlocalization of sheaves former results on diffraction by K. Kataoka.
Reviewer: G.Zampieri


58E20 Harmonic maps, etc.
58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces