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Ellipticity and continuous conormal asymptotics on manifolds with conical singularities. (English) Zbl 0664.58041
The paper develops the theory of elliptic operators with continuous conormal asymptotics. The basic tool is the Mellin transform. A symbolic calculus for Mellin symbols is developed which leads in a natural way to the concept of ellipticity and to parametrix constructions. In a final section the calculus is modified for manifolds with conical singularities.
Reviewer: J.Marschall

MSC:
58J32 Boundary value problems on manifolds
35S15 Boundary value problems for PDEs with pseudodifferential operators
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[1] Agranovič, Uspechi Mat. Nauk 19 pp 53– (1964)
[2] Boutet de Monvel, Acta Math. 126 pp 11– (1971)
[3] Cheeger, Proc. Nat. Acad. Sci. USA 76 pp 2103– (1979)
[4] Costabel, Int. Equ. and Operator Theory 3 pp 323– (1980)
[5] Kondarat’ev, Trudy Mosk. Mat. Obšč. 16 pp 209– (1967)
[6] Kondrat’ev, Uspechi Mat. Nauk 38 pp 3– (1983)
[7] Maz’ja, Zap. naučn. sem. LOMI 52 pp 110– (1975)
[8] Maz’ja, Problems of Math. Anal. 7 pp 100– (1979)
[9] Melrose, Acta Math. 147 pp 149– (1981)
[10] , Elliptic boundary problems in spaces with conical points. Journees ’Equ. Deriv. Part.’ St.-Jean-de-Monts 1981, Conf. No. 4
[11] Plamenevskij, Dokl. Akad. Nauk SSSR 248 pp 2– (1979)
[12] Comm. Part. Diff. Equ. 4, 4 pp 389– (1979)
[13] Rempel, Acad. Sc. 01/84 (1984)
[14] , Complete Mellin symbols and the conormal asymptotics in boundary value problems. Proc. Journees ’Equations aux Dériv. Part.’ St.-Jean-de-Monts 1984, Conf. No. V
[15] Rempel, Ann. Glob. Analysis and Geometry 4, 2 pp 137– (1986)
[16] , Branching of asymptotics for elliptic operators on manifolds on manifolds with edges. Partial Diff. Equ. 1984, Banach Center Publ. Vol. 19 (to appear) · Zbl 0654.58034
[17] , Mellin symbolic calculus and asymptotics for boundary value problems. Seminar Analysis d. Karl-Weierswtraß-Instituts f. Mathematik 1984/85, Berlin 1985
[18] , Asymptotics for elliptic mixed boundary problems; pseudo-differential and Mellin operators in spaces of functions with conormal singularity. Akademie-Verlag Berlin (to appear) · Zbl 0689.35104
[19] Opérateurs pseudo-différentiels et asymptotique sur des variétés à singularités. Séminaire Equations aux Dérivées Partielles 1985–1986, Ecole Polytechnique
[20] Schulze, Preprint der Univ. Bonn, SFB 72
[21] Approx. und Optimierung 777 (1986)
[22] Ziemian, Bull. of the Polish Acad. Sci., Math. 32 pp 3– (1984)
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