On the regular oblique derivative problem for harmonic functions (Q809224)

The regular oblique derivative problem and the mixed Dirichlet-regular oblique derivative problem for harmonic functions in a domain \(\Omega \subset {\mathbb{R}}^ 3\) are considered. It is shown, in particular, that the system of values of an oblique derivative of harmonic homogeneous polynomials is complete in the space \(L_ 2(\partial \Omega)\otimes \{\mu_ 0\}\), where \(\mu\) is the eigenfunction of a certain singular boundary integral equation.