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Mellin expansions of pseudo-differential operators and conormal asymptotics of solutions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1256)

Keywords

  • Elliptic Operator
  • Pseudodifferential Operator
  • Elliptic Boundary
  • Singularity Type
  • Conical Singularity

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. M.F. Atiyah, I.M. Singer: The index of elliptic operators. Ann. of Math. 87 (1968), 484–530

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. L. Boutet de Monvel: Boundary problems for pseudo-differential operators. Acta Math. 126 (1971), 11–51

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. P. Bolley, M. Dauge, J. Camus: Regularité Gevrey pour le problème de Dirichlet dans des domaines à singularités coniques. Comm. Part. Diff. Equ. 10, 4(1985), 391–432

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. J. Brüning, R. Seeley: The resolvent expansion for second order regular singular operators. Preprint No. 80, Univ. Augsburg 1985

    Google Scholar 

  5. J. Cheeger: Spectral geometry of spaces with cone-like singularities. Proc. Nat. Acad. Sci. USA 76 (1979), 2103–2106

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. H.O. Cordes, E.A. Herman: Pseudo-differential operators on a half line. J. Math. Mech. 18 (1969), 893–908

    MathSciNet  MATH  Google Scholar 

  7. M. Costabel: Starke Elliptizität von Randintegraloperatoren erster Art. TH Darmstadt, Preprint 868, 1984

    Google Scholar 

  8. M. Costabel, E. Stephan: A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl. 106 (1985) 367–413

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. G.I. Eskin: Boundary problems for elliptic pseudo-differential equations. Nauka, Moskva 1973 (Transl. of Mathem. Monographs 52, Amer. Math. Soc., Providence, Rhode Island 1980)

    Google Scholar 

  10. L. Hörmander: Pseudo-differential operators and non-elliptic boundary problems. Ann. of Math. 83, 1 (1966), 129–209

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. L. Hörmander: Pseudo-differential operators and hypoelliptic equations. Amer. Math. Soc., Symp. on Singular Integral Operators (1966), 138–183

    Google Scholar 

  12. L. Hörmander: The analysis of linear partial differential operators. I, II, III, IV Grundlehren der Mathem. Wiss., Springer Berlin, Heidelberg, New York, Tokyo 1983–1985

    Google Scholar 

  13. P. Jeanquartier: Transformation de Mellin et développements asymptotiques. L'Enseignement Mathématique 25, 3–4 (1980), 285–308

    MathSciNet  MATH  Google Scholar 

  14. V.A. Kondrat'ev: Boundary value problems for elliptic equations in domains with conical points. Trudy Mosk. Mat. Obšč. 16 (1967) 209–292

    MathSciNet  Google Scholar 

  15. A.I. Komeč: Elliptic boundary problems for pseudo-differential operators on manifolds with conical points. Matem. sb. 86, 2 (1971), 268–298

    Google Scholar 

  16. A.I. Komeč: Elliptic boundary problems on manifolds with piecewise smooth boundary. Matem. sb. 92, 1 (1973), 89–134

    MathSciNet  Google Scholar 

  17. V.A. Kondrat'ev, O.A. Oleynik: Boundary problems for partial differential equations in non-smooth domains. Uspechi Mat. Nauk 38, 2 (1983), 3–76

    Google Scholar 

  18. J.E. Lewis, C. Parenti: Pseudodifferential operators of Mellin type. Comm. Part. Diff. Equ. 8, 5 (1983), 477–544

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. 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. Nachr. 76 (1977), 29–60 (Amer. Math. Soc. Transl. (2) 123, 1984, 57–88)

    CrossRef  MathSciNet  Google Scholar 

  20. 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. Sobolev 1988, 2, Institut Math. Sibirsk. Otdel Akad. Nauk SSSR, Novosibirsk 1978, 69–102 (Amer. Math. Soc. Transl. (2) 123, 1984, 141–170)

    Google Scholar 

  21. R. Melrose, G.A. Mendoza: Elliptic boundary problems in spaces with conical points. Proc. Journees ‘Equ. Dériv. Part.’ St. Jeande-Monts 1981, Conf. 4

    Google Scholar 

  22. R. Melrose, G.A. Mendoza: Elliptic operators of totally characteristic type. MSRI 047-83, Berkeley 1983

    Google Scholar 

  23. Mei-Chi-Shaw: Hodge theory on domains with conic singularities. Comm. in Part. Diff. Equ. 8, 1 (1983), 65–88

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. W. Müller: L2-index of elliptic operators on manifolds with cusps of rank one. Report d.Karl-Weierstraß-Instituts für Mathematik, R-Math-06/85, Berlin 1985

    Google Scholar 

  25. E. Meister: Einige gelöste und ungelöste kanonische Probleme der Beugungstheorie. Preprint No. 918, Techn.Hochschule Darmstadt 1985

    Google Scholar 

  26. B.A. Plamenevskij: On algebras generated by pseudo-differential operators with isolated singularities of symbols. Dokl. Akad. Nauk SSSR 248, 2(1979) (Soviet Math. Dokl. 20, 5 (1979), 1013–1017)

    Google Scholar 

  27. U. Pillat, B.-W. Schulze: Elliptische Randwert-Probleme für Komplexe von Pseudodifferentialoperatoren. Math. Nachr. 94 (1980), 173–210

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. S. Rempel: The index theorem for elliptic transmission problems. Seminar Analysis 1983/84, 141–162, Karl-Weierstraß-Institut für Mathematik, Berlin 1984

    Google Scholar 

  29. S. Rempel, B.-W. Schulze: Index theory of elliptic boundary problems. Akademie Verlag Berlin 1982

    Google Scholar 

  30. S. Rempel, B.-W. Schulze Parametrices and boundary symbolic calculus for elliptic boundary problems without the transmission property. Math. Nachr. 105 (1982), 43–149

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. S. Rempel, B.-W. Schulze: A theory of pseudo-differential boundary value problems with discontinuous conditions I, II. Ann. Glob. Analysis and Geometry 2, 2 (1984), 163–251, 2, 3 (1984), 289–384

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. S. Rempel, B.-W. Schulze: Pseudo-differential and Mellin operators in spaces with conormal singularity (boundary symbols). Report Institute of Mathematics, Acad. Sc. I1/84, Berlin 1984

    Google Scholar 

  33. S. Rempel, B.-W. Schulze: 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

    Google Scholar 

  34. S. Rempel, B.-W. Schulze: Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics. Ann. Glob. Analysis and Geometry 4, 2 (1986), 137–224

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. S. Rempel, B.-W. Schulze: Mellin symbolic calculus and asymptotics for boundary value problems. Seminar Analysis d. Karl-Weierstraß-Instituts für Mathematik 1984/85, Berlin 1985

    Google Scholar 

  36. 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 Verlag Berlin (to appear 1989)

    Google Scholar 

  37. B.-W. Schulze: Ellipticity and continuous conormal asymptotics on manifolds with conical singularities. Prepublications Université de Paris-Sud, Orsay 1986; Math. Nachr. (to appear)

    MATH  Google Scholar 

  38. B.-W. Schulze: Opérateurs pseudo-différentiels et asymptotiques sur des variétés à singularités. Séminaire Equ. aux Dériv. Part., Ecole Polytechnique 1985–1986

    Google Scholar 

  39. B.-W. Schulze: Regularity with continuous and branching asymptotics on manifolds with edges. Preprint des SFB 72, Bonn 1986

    Google Scholar 

  40. B.-W. Schulze: Pseudo-differential operators on manifolds with corners (in preparation)

    Google Scholar 

  41. E. Stephan: Boundary integral equations for mixed boundary value problems, screen and transmission problems in ℝ3. Preprint No. 848, Techn. Hochschule Darmstadt 1984

    Google Scholar 

  42. N. Teleman: The index theorem for topological manifolds. Acta Mathematica 153, 1–2 (1984), 117–152

    CrossRef  MathSciNet  MATH  Google Scholar 

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Schulze, B.W. (1987). Mellin expansions of pseudo-differential operators and conormal asymptotics of solutions. In: Cordes, H.O., Gramsch, B., Widom, H. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077752

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  • DOI: https://doi.org/10.1007/BFb0077752

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