The Dirichlet problem for the dissipative Helmholtz equation in a plane domain bounded by closed and open curves
П. А. Крутицкий · Hiroshima Mathematical Journal · 1998
The Dirichlet problem for the dissipative Helmholtz equation in a connected plane region bounded by closed and open curves is studied.The existence of a classical solution is proved by potential theory.The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.Our approach holds for both internal and external domains.Moreover, domains bounded by closed curves and exterior of open curves in a plane are particular cases of our problem.In case of strongly dissipative Helmholtz equation, the problem is studied under weakened assumptions.