THE DIRICHLET PROBLEM FOR ELLIPTIC-SYSTEMS IN PIECEWISE C(1) PLANE DOMAINS

We study the Dirichlet problem for a strongly elliptic system Lu = 0 with boundary data in L(p)(partial-derivative OMEGA). 1 < p < +infinity, in a piecewise C1 plane domain OMEGA. We show that it is always possible to represent the solution in the form of a double layer potential for which the boundary integral operator is always a Fredholm operator of index 0 for all p, 2 < p < +infinity.