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Book Synopsis
This monograph is devoted to the investigation of boundary properties of the differentiated Poisson integral. It is proved that the boundary properties of the differentiated Poisson integral for different types of domains (circle, sphere, half-plane, half-space, bicylinder) differ substantially from each other and depend on in what sense the integral density is differentiable. The theorems proven here are, in a definite sense, improvable. Relying on the obtained results, the Dirichlet problem is solved for a sphere and a half-space (of a any finite dimension) in the case where the boundary function is measurable and finite almost everywhere.

Boundary Properties & Applications of the

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    A Hardback by Sergo Topuria

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      Publisher: Nova Science Publishers Inc
      Publication Date: Publication Date: 10/08/2009
      ISBN13: 9781606927045, 978-1606927045
      ISBN10: 1606927043

      Description

      Book Synopsis
      This monograph is devoted to the investigation of boundary properties of the differentiated Poisson integral. It is proved that the boundary properties of the differentiated Poisson integral for different types of domains (circle, sphere, half-plane, half-space, bicylinder) differ substantially from each other and depend on in what sense the integral density is differentiable. The theorems proven here are, in a definite sense, improvable. Relying on the obtained results, the Dirichlet problem is solved for a sphere and a half-space (of a any finite dimension) in the case where the boundary function is measurable and finite almost everywhere.

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