SUBSOLUTIONS AND SUPERSOLUTIONS IN A FREE-BOUNDARY PROBLEM

We begin by giving some results of continuity with respect to the doma in for the Dirichlet problem (without any assumption of regularity on the domains). Then, following an idea of A. Beurling, a technique of s ubsolutions and supersolutions for the so-called quadrature surface fr ee boundary problem is presented. This technique would apply to many f ree boundary problems in R(N), N greater-than-or-equal-to 2, which hav e overdetermined Cauchy data on the free boundary. Some applications t o concrete examples are also given.