Address. Mathematical Institute of Czech Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic
E-mail: medkova@math.cas.cz
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