Some boundary properties of a solution of the Poisson equation
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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.
KeywordsPoisson Equation Equilibrium Distribution Borel Measure Green Capacity Subharmonic Function
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- 1.L. Carleson, Selected Problems of Exceptional Set Theory [Russian translation], Mir, Moscow (1971).Google Scholar
- 2.V. I. Danchenko, “Estimates for Green potentials. Application,” Mat. Sb., 194, No. 1, 61–86 (2003)Google Scholar
- 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.G. M. Goluzin, Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).Google Scholar
- 6.V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1976).Google Scholar