##
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

** 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