Abstract
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.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 36, Suzdal Conference-2004, Part 2, 2005.
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Danchenko, D.Y. Some boundary properties of a solution of the Poisson equation. J Math Sci 145, 5192–5196 (2007). https://doi.org/10.1007/s10958-007-0343-7
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DOI: https://doi.org/10.1007/s10958-007-0343-7