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Elliptic theory of differential edge operators. I. (English) Zbl 0745.58045
The paper is concerned with the analysis of general elliptic edge operators with constant indicial roots. This includes Laplacians on asymptotically flat and asymptotically hyperbolic manifolds. Edge operators also arise in boundary problems around higher codimension boundaries. In the first part operators which are semi-Fredholm are studied. It is proved that any element of the nullspace of such an operator has a distributional asymptotic expansion. Conditions are given to guarantee that the coefficients of this expansion are smooth. The results are proved using pseudodifferential operators which incorporate the degeneracies of the edge operators.
Reviewer: J.Marschall

58J05 Elliptic equations on manifolds, general theory
58J32 Boundary value problems on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds
Full Text: DOI
[1] DOI: 10.1215/S0012-7094-81-04804-3 · Zbl 0459.35095 · doi:10.1215/S0012-7094-81-04804-3
[2] Andersson L., Preprint 48 (1989)
[3] H.Friedrich In preparation
[4] DOI: 10.1002/cpa.3160390505 · Zbl 0598.53045 · doi:10.1002/cpa.3160390505
[5] DOI: 10.2307/2374646 · Zbl 0664.58035 · doi:10.2307/2374646
[6] Jour. Func. Anal. 95 pp 225– (1991)
[7] C.Epstein,R. B. Melrose ,Shrinking tubes and the &dstrok-Neumann problem Book, To Appear
[8] G.Mendoza, Resolvent of the Laplacian on strictly pseudoconvex domains To appear, Acta math.
[9] R.Graham ,J.Lee ,Einstien metrics with prescribed conformal infinity on the ball To appear, adv. in Math.
[10] Gilbarg D., ”Elliptic Differential Operators of Second Order (1983) · Zbl 0562.35001
[11] DOI: 10.1007/BF02392727 · Zbl 0496.35042 · doi:10.1007/BF02392727
[12] McOwen R., Preprint 148 (1989)
[13] Mazzeo R., Jour. Diff. Geom 28 pp 309– (1988)
[14] DOI: 10.2307/2374820 · Zbl 0725.58044 · doi:10.2307/2374820
[15] R. Graham,J.Lee, Einstien metrics with prescribed conformal infinity on the ball To appear, adv. in Math. Regularity for the singular Yamabe equation To appear, Indiana Univ. Math. Jour.
[16] DOI: 10.1016/0022-1236(87)90097-8 · Zbl 0636.58034 · doi:10.1016/0022-1236(87)90097-8
[17] Jour. Diff. Geom. 31 pp 185– (1990)
[18] DOI: 10.1215/S0012-7094-90-06021-1 · Zbl 0712.58006 · doi:10.1215/S0012-7094-90-06021-1
[19] N. Smale,Conformally flat metrics of constant postive scalar curvature on subdomains of the sphere To appear, Jour. Diff. Geom · Zbl 0759.53029
[20] McDonald, P. The Laplacian for spaces with cone-like singularities. Thesis. MIT.
[21] DOI: 10.1002/cpa.3160320604 · Zbl 0426.35029 · doi:10.1002/cpa.3160320604
[22] DOI: 10.1080/03605308008820158 · Zbl 0448.35042 · doi:10.1080/03605308008820158
[23] DOI: 10.1007/BF02392873 · Zbl 0492.58023 · doi:10.1007/BF02392873
[24] N.Smale,Conformally flat metrics of constant postive scalar curvature on subdomains of the sphere To appear, Jour. Diff. Geom,Differential analysis on manifolds with corners Book, In Preparation
[25] Mendoza G., MSRI preprint 147 (1983)
[26] DOI: 10.1016/0022-247X(73)90138-8 · Zbl 0272.35029 · doi:10.1016/0022-247X(73)90138-8
[27] Rempel S., Math. Research Series 50 (1989)
[28] Taubes C., L2 moduli spaces on 4-manifolds with cylindrical ends, I, Preprint 50 (1990)
[29] Taylor M., Pseudodifferential Operators · doi:10.1007/978-1-4419-7052-7_1
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