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Ukrainian Mathematical Journal

, Volume 60, Issue 6, pp 831–847 | Cite as

On the smoothness of a solution of the first boundary-value problem for second-order degenerate elliptic-parabolic equations

  • T. S. Gadjiev
  • E. R. Gasimova
Article
  • 39 Downloads

We consider the first boundary-value problem for a second-order degenerate elliptic-parabolic equation with, generally speaking, discontinuous coefficients. The matrix of leading coefficients satisfies the parabolic Cordes condition with respect to space variables. We prove that the generalized solution of the problem belongs to the Hölder space {ie831-01} if the right-hand side f belongs to L p , p > n.

Keywords

Parabolic Equation Classical Solution Space Variable Plane Tangent Closed Domain 
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References

  1. 1.
    M. V. Keldysh, “On some cases of degeneration of equations of elliptic type on the boundary of a domain,” Dokl. Akad. Nauk SSSR, 77, No. 2, 181–183 (1951).Google Scholar
  2. 2.
    G. Fichera, “On a unified theory of boundary-value problems for elliptic-parabolic equations of second order,” in: Boundary-Value Problems in Differential Equations, University of Wisconsin Press, Madison (1960), pp. 97–120.Google Scholar
  3. 3.
    O. A. Oleinik, “On linear second-order equations with nonnegative characteristic form,” Mat. Sb., 69, No. 1, 111–140 (1966).MathSciNetGoogle Scholar
  4. 4.
    M. Franciosi, “Sur di un'equazioni ellittico-parabolico a coefficienti discontinui,” Boll. Unione Mat. Ital., 6, No. 2, 63–75 (1983).Google Scholar
  5. 5.
    A. M. Il'in, “Degenerate elliptic and parabolic equations,” Mat. Sb., 50, No. 4, 443–498 (1960).MathSciNetGoogle Scholar
  6. 6.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).Google Scholar
  7. 7.
    Yu. A. Alkhutov and I. T. Mamedov, “First boundary-value problem for second-order nondivergent parabolic equations with discontinuous coefficients,” Mat. Sb., 131, No. 4, 477–500 (1986).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • T. S. Gadjiev
    • 1
  • E. R. Gasimova
    • 1
  1. 1.Institute of Mathematics and MechanicsNational Academy of Sciences of AzerbaijanBakuAzerbaijan

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