Existence And Uniqueness For The Dirichlet Problem Of The Helmholtz Equation On Unsmoothed Domain

In this paper,we consider the existence and uniquness of solution for Dirichlet problem of the Helmholtz equation on the domain with corners, i.e problemFor smooth boundary,we use potential theory to transform the problem into second kind boundary integral equation ,and use Fredholm alternative theorem,we obtain the existence and uniqueness of Dirichlet problem.For bounded domain with corners,the normal derivative is not continuious which brought some additional difficults.In this paper ,we use modifed potential jump relations to overcome the difRcults.Thereby we obtain the existence and uniqueness for the Dirichlet problem of the Helmholtz equation on domain with corners...