Advances in Analysis

Download PDF (495.7 KB) PP. 114 - 120 Pub. Date: October 25, 2016

DOI: 10.22606/aan.2016.12006

• Artyem Yefimushkin
  Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine

The existence of nonclassical solutions is proved for the Neumann and Poincare problems for generalizations of the Laplace equation in anisotropic and nonhomogeneous media in almost smooth domains with arbitrary boundary data that are measurable with respect to logarithmic capacity. Moreover, it is shown that the spaces of such solutions have the infinite dimension.

Neumann problem, poincare problem, A-harmonic functions, logarithmic capacity, anisotropic and nonhomogeneous media.

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