INDEFINITE ELLIPTIC BOUNDARY-VALUE-PROBLEMS ON IRREGULAR DOMAINS

We establish estimates for the remainder term of the asymptotics of the Dirichlet or Neumann eigenvalue problem -Delta u(x)= lambda r(x) u(x), x is an element of Omega subset of R(n), defined on the bounded open set Omega subset of R(n); here, the ''weight'' r is a real-valued function on Omega which is allowed to change sign in Omega and the boundary partial derivative Omega is irregular. We even obtain error estimates when the boundary is ''fractal''. These results-which extend earlier work of the authors [particularly, J. Fleckinger & M. L. Lapidus, Arch. Rational Mech. Anal. 98 (1987), 329-356; M. L. Lapidus, Trans, Amer. Math. Soc. 325 (1991), 465-529]-are already of interest in the special case of positive weights.