The Poisson Equation with Nonautonomous Semilinear Boundary Conditions in Domains with Many Time Holes
Satoshi Kaizu · SIAM Journal on Mathematical Analysis · 1991
This paper discusses asymptotic behaviors of the solution of the Poisson equation in domains with many tiny holes, where the number of holes grows to infinity and the diameter of each hole tends to zero. The solution satisfies a nonautonomous semilinear boundary condition on fragmentary boundaries of many tiny holes. Sufficient conditions are given, under which an extension of the solution to the domain with no hole converges, and the equation satisfied by the limit of the extension of the solution is determined. The convergence properties of Radon measures are applied, and also the convergence properties of the resolvent of subdiflerentials together with variational inequalities are applied.