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 a special 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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The author would like to thank the referee for his useful proposals on the improvement of the text.
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Ryazanov, V. On Neumann and Poincare problems for Laplace equation. Anal.Math.Phys. 7, 285–289 (2017). https://doi.org/10.1007/s13324-016-0142-8
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DOI: https://doi.org/10.1007/s13324-016-0142-8
Keywords
- Neumann and Poincare problems
- Laplace equation
- Harmonic functions
- Directional derivatives
- Nontangential limits