Advertisement

Asymptotic formulas for solutions of nonlocal elliptic problems

  • A. L. Skubachevskii
Article

Abstract

We consider nonlocal elliptic problems in plane domains and obtain asymptotic formulas for solutions in weighted spaces near junction points.

Keywords

Weak Solution Vector Function STEKLOV Institute Operator Function Asymptotic Formula 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. V. Bitsadze and A. A. Samarskii, “On Some Simple Generalizations of Linear Elliptic Boundary Problems,” Dokl. Akad. Nauk SSSR 185(4), 739–740 (1969) [Sov. Math., Dokl. 10, 398–400 (1969)].MathSciNetGoogle Scholar
  2. 2.
    A. A. Samarskii, “Some Problems in Differential Equation Theory,” Diff. Uravn. 16(11), 1925–1935 (1980) [Diff. Eqns. 16, 1221–1228 (1981)].MathSciNetGoogle Scholar
  3. 3.
    A. L. Skubachevskii, “Elliptic Problems with Nonlocal Conditions near the Boundary,” Mat. Sb. 129(2), 279–302 (1986) [Math. USSR, Sb. 57 (1), 293–316 (1987)].MathSciNetGoogle Scholar
  4. 4.
    V. A. Kondrat’ev, “Boundary Problems for Elliptic Equations in Domains with Conical or Angular Points,” Tr. Mosk. Mat. Obshsch. 16, 209–292 (1967) [Trans. Mosc. Math. Soc. 16, 227–313 (1967)].MATHGoogle Scholar
  5. 5.
    P. L. Gurevich, “Asymptotics of Solutions for Nonlocal Elliptic Problems in Plane Angles,” Tr. Semin. im. I.G. Petrovskogo 23, 93–126 (2003) [J. Math. Sci. 120 (3), 1295–1312 (2004)].Google Scholar
  6. 6.
    A. P. Soldatov, “The Bitsadze-Samarskii Problem for Douglis Analytic Functions,” Diff. Uravn. 41(3), 396–407 (2005) [Diff. Eqns. 41, 416–428 (2005)].MathSciNetGoogle Scholar
  7. 7.
    A. L. Skubachevskii, Nonclassical Boundary-Value Problems. I (Ross. Univ. Druzhby Nar., Moscow, 2007), Sovrem. Mat., Fundam. Napravl. 26 [J. Math. Sci. 155 (2), 199–334 (2008)]; II (Ross. Univ. Druzhby Nar., Moscow, 2009), Sovrem. Mat., Fundam. Napravl. 33 [J. Math. Sci. 166 (4), 377–561 (2010)].Google Scholar
  8. 8.
    S. Agmon, A. Douglis, and L. Nirenberg, “Estimates near the Boundary for Solutions of Elliptic Partial Differential Equations Satisfying General Boundary Conditions. I,” Commun. Pure Appl. Math. 12, 623–727 (1959).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    P. Gurevich, “Smoothness of Generalized Solutions for Higher-Order Elliptic Equations with Nonlocal Boundary Conditions,” J. Diff. Eqns. 245(5), 1323–1355 (2008).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations