Pseudo-differential operators on manifolds with edges. (English) Zbl 0693.58026
Partial differential equations, Proc. Symp., Holzhau/GDR 1988, Teubner-Texte Math. 112, 259-288 (1989).
[For the entire collection see Zbl 0665.00006.]
The author studies elliptic boundary value problems on manifolds with edges. Near an edge such a manifold looks essentially like \({\bar {\mathbb{R}}}_+\times X\times {\mathbb{R}}^ q\) for some closed compact \(C^{\infty}\)-manifold X. For simplicity it is assumed that \(\partial X=\emptyset\). As main tools, edge Sobolev spaces with continuous asymptotics and edge pseudo-differential operators are introduced and studied.
The author studies elliptic boundary value problems on manifolds with edges. Near an edge such a manifold looks essentially like \({\bar {\mathbb{R}}}_+\times X\times {\mathbb{R}}^ q\) for some closed compact \(C^{\infty}\)-manifold X. For simplicity it is assumed that \(\partial X=\emptyset\). As main tools, edge Sobolev spaces with continuous asymptotics and edge pseudo-differential operators are introduced and studied.
Reviewer: J.Marschall
MSC:
| 58J40 | Pseudodifferential and Fourier integral operators on manifolds |
| 35J55 | Systems of elliptic equations, boundary value problems (MSC2000) |
| 35S99 | Pseudodifferential operators and other generalizations of partial differential operators |
