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The dirichlet problem in weighted spaces and some uniqueness theorems for harmonic functions

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Abstract

This paper considers the Dirichlet problem in weighted spaces L 1(ρ) in the half-plane and in the disk. The obtained results are applied to studying the uniqueness questions of harmonic functions in the half-plane and in the half-space. Also, the uniqueness theorem of harmonic functions in the unit disk is proved.

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Correspondence to G. M. Airapetyan.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 67, Partial Differential Equations, 2010.

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Airapetyan, G.M. The dirichlet problem in weighted spaces and some uniqueness theorems for harmonic functions. J Math Sci 173, 123–149 (2011). https://doi.org/10.1007/s10958-011-0235-8

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