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The Vishik-Lyusternik method for elliptic boundary-value problems in regions with conical points

II. The problem in a bounded region

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Literature Cited

  1. M. I. Vishik and L. A. Lyusternik, “Regular degeneracy and boundary layer for linear differential equations with a parameter,” Usp. Mat. Nauk,12, No. 5, 3–192 (1957).

    Google Scholar 

  2. V. A. Trenogin, “Development and applications of asymptotic method of Vishik-Lyusternik,” Usp. Mat. Nauk,25, No. 4, 123–156 (1970).

    Google Scholar 

  3. P. L. Cook and G. S. Ludford, “The behavior as of solutions to ɛ∇2w = (∂/∂y)w on the rectangle 0≤x≤l, |y|≤1,” SIAM J. Math. Anal.,2, No. 4, 161–184 (1971).

    Google Scholar 

  4. V. F. Butuzov, “Asymptotic behavior of solution of equationμ 2Δu − k2(x, y)u = f(x, y) in a rectangular region,” Differents. Uravn.,9, No. 9, 1654–1660 (1973).

    Google Scholar 

  5. A. M. Il'in and E. F. Delikova, “Method of coalescence of asymptotic representations for the equation ɛ2Δu − a(x, y)uy = f(x,y) in a rectange,” Mat. Sb.,96, No. 4, 568–583 (1975).

    Google Scholar 

  6. S. A. Nazarov, “Asymptotic behavior with respect to small parameter of solution of elliptic boundaryvalue problem in region with conical point,” Dokl. Akad. Nauk SSSR,238, No. 5, 827–830 (1978).

    Google Scholar 

  7. M. S. Agranovich and M. I. Vishik, “Elliptic problems with a parameter and parabolic problems of general form,” Usp. Mat. Nauk,19, No. 3, 53–160 (1964).

    Google Scholar 

  8. S. A. Nazarov, “The Vishik-Lyusternik method for elliptic boundary-value problems in regions with conical points. I. The problem in a cone, Sib. Mat. Zh.,22, No. 4 (1981).

  9. J. L. Lions and E. Magenes, Non-Homogeneous Boundary-Value Problems and Applications, Springer-Verlag (1972).

  10. V. A. Kondrat'ev, “Boundary-value problems for elliptic equations in regions with conical or corner points,” Tr. Mosk. Mat. O-va,16, 219–292 (1967).

    Google Scholar 

  11. V. G. Maz'ya and B. A. Plamenevskii, “Coefficients in the asymptotic expressions of the solutions of elliptic boundary-value problems in regions with conical points,” Math. Nachr.,76, 29–60 (1977).

    Google Scholar 

  12. V. A. Kondrat'ev, “Solvability of first boundary-value problem for strongly elliptic equations,” Tr. Mosk. Mat. O-va,16, 298–318 (1967).

    Google Scholar 

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Authors
  1. S. A. Nazarov
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Additional information

A. A. Zhdanov Leningrad State University. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 22, No. 5, pp. 132–152, September–October, 1981.

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Nazarov, S.A. The Vishik-Lyusternik method for elliptic boundary-value problems in regions with conical points. Sib Math J 22, 753–769 (1981). https://doi.org/10.1007/BF00968072

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  • DOI: https://doi.org/10.1007/BF00968072

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