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Journal of Mathematical Sciences

, Volume 172, Issue 3, pp 401–421 | Cite as

The dirichlet problem for harmonic functions from variable exponent smirnov classes in domains with piecewise smooth boundary

  • V. Kokilashvili
  • V. Paatashvili
Article

The Dirichlet problem is solved for harmonic functions from variable exponent Smirnov classes in domains with piecewise smooth boundaries. The solvability conditions are established. Depending on the boundary geometry and value of the space exponent at angular points, the Dirichlet problem may turn out to be unsolvable, solvable uniquely and non-uniquely. In the unsolvable case, for boundary functions the necessary and sufficient conditions are found, which govern the solvability. In all solvability cases, solutions are constructed in explicit form. Bibliography: 19 titles.

Keywords

Harmonic Function Dirichlet Problem Conformal Mapping Homogeneous Problem Variable Exponent 
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.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.A. Razmadze Mathematical InstituteTbilisiGeorgia
  2. 2.I. Javakhishvili Tbilisi State UniversityTbilisiGeorgia

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