The Dirichlet Problem for the Equation Δu−k2u=0 in the Exterior of Nonclosed Lipschitz Surfaces

الملخص EN

We study the Dirichlet problem for the equation Δu−k2u=0 in the exterior of nonclosed Lipschitz surfaces in R3.

The Dirichlet problem for the Laplace equation is a particular case of our problem.

Theorems on existence and uniqueness of a weak solution of the problem are proved.

The integral representation for a solution is obtained in the form of single-layer potential.

The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.