Elliptic Boundary Value Problems

Part of the Texts in Applied Mathematics book series (TAM, volume 50)


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7.6 Guide to the Literature

  1. 36.
    de Jager, E.M. and Jiang Furu (1996), The Theory of Singular Perturbations, Elsevier, North-Holland Series in Applied Mathematics and Mechanics 42, Amsterdam.Google Scholar
  2. 41.
    Dorr, F.W., Parter, S.V., and Shampine, L.F. (1973), Application of the maximum principle to singular perturbation problems, SIAM Rev. 15, pp. 43–88.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 43.
    Eckhaus, W. (1979), Asymptotic Analysis of Singular Perturbations, North-Holland, Amsterdam. Chapter 7zbMATHGoogle Scholar
  4. 45.
    Eckhaus, W. and de Jager, E.M. (1966), Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rat. Mech. Anal. 23, pp. 26–86.zbMATHCrossRefGoogle Scholar
  5. 64.
    Grasman, J. (1971), On the Birth of Boundary Layers, Mathematical Centre Tract 36, Amsterdam.Google Scholar
  6. 65.
    Grasman, J. (1974), An elliptic singular perturbation problem with almost characteristic boundaries, J. Math. Anal. Appl. 46, pp. 438–446.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 68.
    Grasman, J. and van Herwaarden, O.A. (1999), Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications, Springer-Verlag, New York.zbMATHGoogle Scholar
  8. 88.
    Huet, D. (1977), Perturbations singulières de problèmes elliptiqes, in Lecture Notes in Mathematics 594 (Brauner, C.M., Gay, B., and Mathieu, J., eds.), Springer-Verlag, Berlin.Google Scholar
  9. 91.
    Il’in, A.M. (1999), The boundary layer, in Partial Differential Equations V, Asymptotic Methods for Partial Differential Equations (Fedoryuk, M.V., ed.), Encyclopaedia of Mathematical Sciences 34, Springer-Verlag, New York.Google Scholar
  10. 121.
    Levinson, N. (1950), The first boundary value problem for εΔu+A(x, y)ux+B(x, y)uy+C(x, y)u=D(x, y) for small ε, Ann. Math. 51, pp. 428–445.CrossRefMathSciNetGoogle Scholar
  11. 123.
    Lions, J.L. (1973), Perturbations singulières dans les Problèmes aux Limites et en Contrôle Optimal, Lecture Notes in Mathematics 323, Springer-Verlag, Berlin.zbMATHGoogle Scholar
  12. 165.
    Sanchez Hubert, J. and Sanchez Palencia, E. (1989), Vibration and Coupling of Continuous Systems: Asymptotic Methods, Springer-Verlag, New York.zbMATHGoogle Scholar
  13. 184.
    Trenogin, V.A. (1970), Development and applications of the asymptotic method of Liusternik and Vishik, Usp. Mat. Nauk 25, pp. 123–156; transl. in Russ. Math. Surv. 25, pp. 119–156.zbMATHMathSciNetGoogle Scholar
  14. 197.
    Van Harten, A. (1978), Nonlinear singular perturbation problems: proofs of correctness of a formal approximation based on a contraction principle in a Banach space, J. Math. Anal. Appl. 65, pp. 126–168.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 214.
    Vishik, M.I. and Liusternik, L.A. (1957), On elliptic equations containing small parameters in the terms with higher derivatives, Dokl. Akad. Nauk, SSR, 113, pp. 734–737.zbMATHGoogle Scholar

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