Displaying similar documents to “On the boundary values of harmonic functions.”

Infinite dimension of solutions of the Dirichlet problem

Vladimir Ryazanov (2015)

Open Mathematics

Similarity:

It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

The boundary-value problems for Laplace equation and domains with nonsmooth boundary

Dagmar Medková (1998)

Archivum Mathematicum

Similarity:

Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.

The successive approximation method for the Dirichlet problem in a planar domain

Dagmar Medková (2008)

Applicationes Mathematicae

Similarity:

The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.