L2-INTEGRABILITY OF 2ND-ORDER DERIVATIVES FOR POISSON EQUATION IN NONSMOOTH DOMAINS

We define a certain class of domains with corners directed outwards only, thus being natural extensions of convex domains. We show that such a domain OMEGA can be approximated with smooth domains OMEGA(m) of the same type, Using a technique based on integration by parts we derive an a priori estimate //u//H-2(OMEGAm) less-than-or-equal-to C(OMEGA) //DELTAu//L2(OMEGAm) for u is-an-element-of H-2(OMEGA(m)) and H-0(1)(OMEGA(m)) where C(OMEGA) is independent of m. This enables us to obtain a solution u in H-2(OMEGA) of the Dirichlet problem [GRAPHICS] Here gamma is the trace operator on the boundary of OMEGA.