On nonexisting solutions for Dirichlet problem and MAC
Igor Neygebauer · 2011
The Dirichlet problem for Laplace equation is considered. The nonexisting solution of the problem for unbounded domain is analyzed. If the domain is a ring then the solution exist. But if the outer boundary of a ring tends to infinity then the solution of the Dirichlet problem does not exist for different boundary values on the inner and outer boundaries. The method of additional conditions (MAC) can give bounded solutions of Dirichlet problem in the case of angle and corner singularities in classical consideration of the problem. In this paper MAC is applied to obtain the physically understandable solution also in this case of classically nonexisting solution. The solution could be considered as the solution of a bad posed Cauchy problem for Laplace equation.