Opérateurs pseudo-différentiels et asymptotique sur des variétés à singularités

 Access to full text

 Full (PDF)

1. [A1] M.S. Agranovič, M.I. Višik: Elliptic problems with a parameter and parabolic problems of general type. Uspechi Mat. Nauk19, 3 (1964) 53-161 (English trans1. in Russian Math. Surveys19 (1964)) Zbl0137.29602MR192188
2. [B1] L. Boutet de Monvel: Boundary problems for pseudo-differential operators. Acta Math.126 (1971) 11-51. Zbl0206.39401MR407904
3. [B2] M.S. Baouendi, J. Sjöstrand: Régularité analytique pour des opérateurs elliptiques singuliers en un point. Ark. for Math.14 (1976) 9-33. Zbl0334.35021MR466958
4. [B3] P. Bolley, M. Dauge, J. Camus: Régularité Gevrey pour le problème de Dirichlet dans des domaines à singularités coniques. Comm. Part. Diff. Equ.10, 4 (1985) 391-432. Zbl0573.35024MR784683
5. [C1] J. Cheeger: Spectral geometry of spaces with cone-like singularities. Proc. Nat. Acad. Sci. USA76 (1979) 2103-2106. Zbl0411.58003MR530173
6. [C2] M. Costabel: Singular integral operators on curves with corners. Int. Equ. and Operator Theory3 (1980) 323-349. Zbl0445.45025MR580713
7. [D1] M. Dauge: Second membre analytique pour un problème aux limites elliptique d'ordre 2m sur un polygône. Comm. Part. Diff. Equ.9, 2 (1984) 169-195. Zbl0549.35037MR736414
8. [G1] P. Grisvard: Boundary value problems in domains with non smooth boundaries. Lecture Notes 19, Univ. of Maryland1980. 
9. [G2] P. Grisvard: Singularités des problèmes aux limites dans des polyèdres. Séminaire Goulaouic-Meyer-Schwartz1981/82, n°8. Zbl0499.35038MR671605
10. [J1] P. Jeanquartier: Transformation de Mellin et développements asymptotiques. L'Enseignement Mathématique25, 3-4 (1980) 285-308. Zbl0436.46031MR570314
11. [K1] V.A. Kondrat'ev: Boundary value problems for elliptic equations in domains with conical points. Trudy Mosk. Mat. Obšč.16 (1967) 209-292 (Transactions Moscow Math. Soc. (1967) 227-313). Zbl0194.13405MR226187
12. [L1] J.E. Lewis, C. Parenti: Pseudodifferential operators of Mellin type. Comm. Part. Diff. Equ.8, 5 (1983) 477-544. Zbl0532.35085MR695401
13. [M1] V.G. Maz'ja, B.A. Plamenevskij: On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Math. Nach.76 (1977) 29-60 (Amer. Math. Soc. Transl. (2) 123, 1984, pp. 57-88). Zbl0554.35036MR601608
14. [M2] V.G. Maz'ja, B.A. Plamenevskij: Weighted spaces with nonhomogeneous norms, and boundary value problems in domains with conical points. Ellipt. Diff. gleichungen, Meeting Rostock 1977, Univ. Rostock1978, 161-189 (Amer. Math. Soc. Transl. (2) 123, 1984, pp 89-108). Zbl0429.35031MR540196
15. [M3] V.G. Maz'ja, B.A. Plamenevskij: Schauder estimates of solutions of elliptic boundary value problems in domains with edges on the boundary. Part. Diff. Equ., Proc. Sem. S.L. Sobolev1978; 2, Institut Math. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk1978, 69-102 (Amer. Math. Soc. Transl. (2) 123, 1984, pp.141-170). Zbl0554.35038MR568035
16. [M4] R. Melrose: Transformation of boundary problems. Acta Math.147 (1981) 149-236. Zbl0492.58023MR639039
17. [M5] R. Melrose, G.A. Mendoza: Elliptic boundary problems in spaces with conical points. Proc. Journées "Equ. Dériv. Part." St. Jean de Monts 1981, Conf.4. Zbl0481.35004
18. [NI] V.A. Nikiščin: Singularities of the solution to the Dirichlet problem for a second order equation in a neighbourhood of an edge. Vestnik Moscov Univ. Mat.34, 2 (1979) 51-62 (Moscov Univ. Math. Bull.34, 2 (1979) 53-64). Zbl0497.35031MR531648
19. [P1] B.A. Plamenevskij: On algebras generated by pseudodifferential operators with isolated singularities of symbols. Dokl. Akad. Nauk SSSR248, 2 (1979) (Soviet Math. Dokl.20, 5 (1979) 1013-1017). Zbl0449.58020MR553193
20. [P2] Pham The Lai: Problème de Dirichlet dans un cône avec paramètre spectral pour une classe d'espaces de Sobolev à poids. Comm. Part. Diff. Equ.4 (1979) 389-445. Zbl0498.35022MR525776
21. [P3] Pham The Lai: Nouveau regard sur un travail de Kondrat'ev. Séminaire Equ. aux Dériv. Part. Nantes1981/ 82, I.6. 
22. [R1] S. Rempel,B.-W. Schulze: Parametrices and boundary symbolic calculus for elliptic boundary problems without the transmission property. Math. Nachr.105 (1982) 45-149. Zbl0544.35095MR670511
23. [R2] S. Rempel, B.-W. Schulze: Complete Mellin symbols and the conormal asymptotics in boundary value problems. Proc. Journees "Equ. Dériv. Part."St-Jean de Monts1984, Conf.5. Zbl0598.35022
24. [R3] S. Rempel, B.-W. Schulze: Branching of asymptotics for elliptic operators on manifolds with edges. Banach Center Publ. Proc. of the Semester "Part. Diff. Equ."1984, vol. 19 (to appear). Zbl0654.58034MR1055175
25. [R4] S. Rempel, B.-W. Schulze: Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics. Ann. Global Anal. and Geometry (to appear 1986). Zbl0632.58032MR910551
26. [R5] S. Rempel, B.-W. Schulze: Mellin symbolic calculus and asymptotics for boundary value problems. Seminar Analysis 1984/85 des Karl-Weierstrass-Instituts, Berlin1985. Zbl0595.31012MR896489
27. [R6] S. Rempel, B.-W. Schulze: Asymptotics for elliptic mixed boundary problems (pseudo-differential and Mellin operators in spaces with conormal singularity). Math. Research Series, Akademie-VerlagBerlin (to appear 1986). Zbl0689.35104MR1002573
28. [S1] B.-W. Schulze: Ellipticity and continuous conormal asymptotics on manifolds with conical singularities. Preprint 1985. Zbl0664.58041MR952461

1. B. W. Schulze, Corner Mellin operators and reduction of orders with parameters