On Neumann and Poincare problems for Laplace equation

2015/10/03 by Ryazanov, Vladimir
#31A20 #31A25 #31B25 #31C05 #34M50 #35F45 #35Q15 #Complex Variables (math.CV) #FOS: Mathematics #primary 31A05 #secondary 30E25

paper · doi:10.48550/arxiv.1510.00733

Abstract

It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for the partial case of the Poincare problem on directional derivatives. Moreover, it is shown that the spaces of the found solutions have the infinite dimension.

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