On Neumann and Poincare problems in mathematical physics

Abstract

It is proved the existence of nonclassical solutions of 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 measureable with respect to logarithmic capacity. Moreover, it is shown that the spaces of such solutions have the infinite dimension.

arXiv comment14 pages. arXiv admin note: text overlap with arXiv:1511.02798; text overlap with arXiv:1510.00733 by other authors