The Dirichlet Problem for the Semilinear Vibrating String Equation in a Class of Domains with Corner Points

This paper deals with existence, uniqueness, and regularity of solutions of the Dirichlet problem for the semilinear vibrating string equation in a class of bounded domains with corner points, Under some symmetry conditions on the boundary we reduce our problem to the corresponding problem in a rectangle. Using known results for rectangular domains, existence, uniqueness, and regularity of solutions are obtained.