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Original Articles

On elliptic boundary value problems on upper half-plane

Pages 719-731 | Received 16 Feb 2005, Published online: 30 Aug 2006

References

References

  • Soldatov AP 2003 On the first and second boundary value problems for elliptic systems on the plane Differentcial'nye Uravneniya 39 674 686 (in Russian)
  • Bitsadze AV 1968 Boundary Value Problems for Elliptic Equations of Second Order Amsterdam North Holland Publ. Co.
  • Soldatov AP 1999 To elliptic theory for domains with piecewise smooth boundary on the plane Proc. the Congress ISAAC'97 3 7 June 1997 University of Delaware Newark USA Partial Diff. and Integr. equations, pp. 177–186, Kluver Ac. Publ
  • Vishik MI 1951 On strong elliptic systems of differential equations Matematicheskiy Sbornik 29 3 615 676 (in Russian)
  • Somigliano , C . 1884 . Sui sistemi simmetrici di equazioni a derivate parziali . Ann. Math. II , 22 : 143 – 156 .
  • Soldatov AP Mitin SP 1997 On some class of strongly elliptic systems Differentcial'nye Uravneniya 33 1118 1122 (in Russian)
  • Douglis , AA . 1953 . A function-theoretic approach to elliptic systems of equations in two variables . Communications on Pure and Applied Mathematics , 6 : 259 – 289 .
  • Soldatov AP 1993 A generalized Cauchy type integral and singular integral in Holder spaces with a weight Doklady Akademii Nauk SSSR 330 164 166 (in Russian)
  • Mushelishvili NI 1953 Singular Integral Equations Groningen Noordhoff 
  • Gakhov FD 1962 Boundary Value Problems Oxford Pergamon
  • Vekua NP 1967 Systems of Singular Integral Equations Groningen, Leyden Netherlands Noordhoof Int.
  • Soldatov AP 2002 The problem R for Lavrent'ev-Bitsadze system in the weighted Hardy spaces Differentcial'nye Uravneniya 38 1418 1430 (in Russian)
  • Bitsadze AV 1948 On uniqueness solution of the Dirichlet problem for elliptic equations with partial derivatives Uspehi Matematicheskih Nauk 3 6 153 154 (in Russian)
  • Mushelishvili NI 1953 Some Basic Problems of the Mathematical Theory of Elasticity Groningen Noordhoff
  • Kupradze VD 1965 Potential Methods in the Theory of Elasticity Jerusalem Israel Program Sc. Transl.
  • Soldatov AP 2002 Lame system of anisotropic plane elasticity Dokl. RAN 385 163 167 (in Russian)
  • Begehr H Lin Wei 1992 A mixed–contact problem in orthotropic elasticity In: H. Begerhand and A. Jeffrey (Eds) Partial Differential Equations with Real Analysis Harlow Longman Scientific & Technical pp. 219–239
  • Gilbert RP 1981 Plane Ellipticity and Related Problems Providence Rl American Mathematical Society
  • Gilbert , RP and Lin , Wei . 1985 . Function theoretical solutions to problems of orthotropic elasticity . Journal of Elasticity , 15 : 143 – 154 .

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