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Original Articles

On a Dirichlet problem for one improperly elliptic equation

Pages 825-837 | Received 22 Jun 2018, Accepted 07 Oct 2018, Published online: 01 Feb 2019

References

  • Lions J-L, Magenes E. Problemes aux limites non homogenes at applications, v.1. Paris: Dunod; 1968.
  • Gohberg I, Krein M. Fundamental aspects of defect numbers, root numbers and indices of linear operators. Uspekhi Math Nauk [Russian Math. Surveys]. 1957;12(2(74)):43–118.
  • Bitsadze AV. On the uniqueness of the solution of the Dirichlet problem for partial differential equations of elliptic type. Uspekhi Math Nauk [Russian Math Surveys]. 1948;3(6):211–212.
  • Bitsadze AV. Boundary value problems for second order elliptic equations. Moscow: Nauka; 1966. (Russian)
  • Tovmasyan NE. The general boundary value problem for second order elliptic systems with constants coefficients. Differencialnye Uravneniya. 1966;2(1):3–23. (Russian)
  • Tovmasyan NE. The general boundary value problem for second order elliptic systems with constants coefficients II. Differencialnye Uravneniya. 1966;2(2):163–171. (Russian)
  • Soldatov AP. A function theory method in boundary value problems in the plane. I The smooth case. Math USSR – Izvestiya. 1992;39(2):1033–1061. doi: 10.1070/IM1992v039n02ABEH002236
  • Soldatov AP. A function theory method in elliptic problems in the plane. II The piecewise smooth case. Russ Acad Sci Izvestiya Math. 1993;40(3):529–563. doi: 10.1070/IM1993v040n03ABEH002176
  • Lopatinskii YB. On a method of reduction of the boundary value problem for the elliptic type system of partial differential equations to regular integral equations. Ukrainian Math J. 1953;5:123–151. (Russian)
  • Volpert AI. On an index and normal solvability of the boundary value problems for elliptic systems of differential equations on the plane. Trudy Moskovskogo Matematicheskogo Obschestva [Proceedings of Moscow Mathematical Society]. 1961;10:41–87. (Russian)
  • Soldatov AP. The Neumann problem for elliptic systems on the plane. Sovremennaya matematika Fundamentalny e napravleniya. 2013;48:120–133. (Russian) [J Math Sci.]; 2014; 202(6):897–910.
  • Begehr H, Kumar A. Boundary value problems for the inhomogeneous poly-analytic equation. I. Analysis. 2005;25(1):55–71. doi: 10.1515/anly-2005-0103
  • Tovmasyan NE. New statement and investigation of the I, the II and the III boundary problems for two second order elliptic strongly bounded systems of differential equations. Izvestiya AN ArmSSR Matematika. 1968;3(6):498–521. (Russian)
  • Tovmasyan NE. Non-regular differential equations and calculations of electromagnetic fields. Singapore: World Scientific; 1998.
  • Babayan AH. O zadache Dirihle dlya nepravilno ellipticheskogo uravneniya chetvertogo poryadka. [On a Dirichlet problem for fourth order improperly elliptic equation]. Neklassicheskije uravnenija matematicheskoj fiziki [Nonclassical equations of mathematical physics]. Novosibirsk: Izd. Mathem. Inst.; 2007; 56–69.
  • Babayan AH. The Dirichlet problem for a fourth order partial differential equation in the case of double roots of the characteristic equation. Mathematica Montisnigri. 2015;32:66–80. (Russian)
  • Babayan AH, Mohammadi MH. On the Dirichlet problem for one properly elliptic equation in the unit disk. Reports NAS of Armenia. 2017;117(3):192–199. (Russian)
  • Burskii VP, Buryachenko EA. Some aspects of the non-trivial solvability of the homogeneous Dirichlet problems for linear equations of arbitrary even order in the unit disk. Math Notes. 2005;77(3):461–470. (Russian) doi: 10.1007/s11006-005-0044-9
  • Babayan AH. Dirichlet problem for properly elliptic equation in the unit disk. Izvestiya NAN Armenii, Matematika. 2003;38(6):39–48.
  • Axler S, Bourdon B, Ramey W. Harmonic function theory. New York: Springer-Verlag. Inc; 2001.
  • Bari NK. Trigonometric series. Moscow: Nauka; 1961. (Russian)

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