Journal of Mathematical Sciences

, Volume 145, Issue 5, pp 5192–5196 | Cite as

Some boundary properties of a solution of the Poisson equation

  • D. Ya. Danchenko


Certain boundary properties of a solution u of the boundary-value problem for the Poisson equation Δ u = f in a disk are studied. In particular, various estimates for integral norms of the solution through the Green capacity of the condenser composed of the support of the function f and the boundary of the disk and also through the growth rate of the function f are given. The proofs are based on the theorem on coverings of supports of Borel measures outside of which the Green potentials of these measures are bounded by unity.


Poisson Equation Equilibrium Distribution Borel Measure Green Capacity Subharmonic Function 
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  1. 1.
    L. Carleson, Selected Problems of Exceptional Set Theory [Russian translation], Mir, Moscow (1971).Google Scholar
  2. 2.
    V. I. Danchenko, “Estimates for Green potentials. Application,” Mat. Sb., 194, No. 1, 61–86 (2003)Google Scholar
  3. 3.
    D. Ya. Danchenko, Certain problems of approximation and interpolation by rational function. Application to equations of elliptic type, Dissertation [in Russian], Vladimir State Pedagogical Institute, Vladimir (2001).Google Scholar
  4. 4.
    G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).Google Scholar
  5. 5.
    W. Hayman and P. Kennedy, Subharmonic Functions [Russian translation], Mir, Moscow (1980).MATHGoogle Scholar
  6. 6.
    V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1976).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • D. Ya. Danchenko
    • 1
  1. 1.Vladimir State UniversityRussia

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