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On one boundary-value problem for a strongly degenerate second-order elliptic equation in an angular domain

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Abstract

We prove the existence and uniqueness of a classical solution of a singular elliptic boundary-value problem in an angular domain. We construct the corresponding Green function and obtain coercive estimates for the solution in the weighted Hölder classes.

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References

  1. V. A. Kondrat’ev, “Boundary-value problems for elliptic equations in domains with conic or angular points,” Tr. Mosk. Mat. Obshch., 16, 209–292 (1967).

    MATH  Google Scholar 

  2. S. Z. Levendorskii and B. G. Paneyakh, “Degenerate elliptic equations and boundary-value problems,” in: VINITI Series in Contemporary Problems of Mathematics (Fundamental Trends) [in Russian], Vol. 63, VINITI, Moscow (1990), pp. 131–200.

    Google Scholar 

  3. M. I. Matiichuk, Parabolic and Elliptic Boundary-Value Problems with Singularities [in Ukrainian], Prut, Chernivtsi (2003).

    Google Scholar 

  4. P. Grisvard, Elliptic Problem in Nonsmooth Domain, Pitman, London (1985).

    Google Scholar 

  5. V. Maz’ya, S. Nazarov, and B. Plamenevskij, Asymptotic Theory of Elliptic Boundary-Value Problems in Singular Perturbed Domains, Birkhäuser, Basel (2000).

    Google Scholar 

  6. C. Goalaouic and N. Shimakura, “Regularite Hölderienne de certains problemes aux limites ellipticues degeneres,” Ann. Scuola Norm. Super. Pisa. IV, 10, No. 1 79–108 (1983).

    Google Scholar 

  7. D. Gubelidze, “On a generalized solution of the second-order degenerate elliptic equation in an angular domain,” Proc. A. Razmadze Math. Inst., 133, 37–61 (2003).

    MATH  MathSciNet  Google Scholar 

  8. B. V. Bazalii and N. V. Krasnoshchek, “Regularity of a solution of a multidimensional problem with free boundary for the equation of porous medium,” Mat. Tr., 5, No. 2, 38–91 (2002).

    MathSciNet  Google Scholar 

  9. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  10. M. V. Fedoryuk, Saddle-Point Method [in Russian], Nauka, Moscow (1977).

    MATH  Google Scholar 

  11. O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  12. B. V. Bazalii and N. V. Krasnoshchek, “Regularity of a solution of a problem with free boundary for the equation υt = (υm)xx,” Alg. Analiz, 12, Issue 2, 1–21 (2000).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    B. V. Bazalii & S. P. Degtyarev

Authors
  1. B. V. Bazalii
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  2. S. P. Degtyarev
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 867–883, July, 2007.

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Bazalii, B.V., Degtyarev, S.P. On one boundary-value problem for a strongly degenerate second-order elliptic equation in an angular domain. Ukr Math J 59, 955–975 (2007). https://doi.org/10.1007/s11253-007-0062-8

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  • DOI: https://doi.org/10.1007/s11253-007-0062-8

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