The Boundary-Value Problems for Laplace Equation and Domains with Nonsmooth Boundary

Dagmar Medkova

Address. Mathematical Institute of Czech Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic


Abstract. 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.

AMS classification. 35J05, 35J25, 31B10

Key words. Laplace equation, Dirichlet problem, Neumann problem, Robin problem