On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems

Abstract

A perturbation of the Poisson equation by a biharmonic operator with a small multiplier ε is considered. The asymptotic behavior of the solution of the Dirichlet problem for this equation as ε → 0 is studied. The gradient of the solution is proved to converge to the gradient of the solution to Poisson equation in L₁ (Ω) as ε → 0. The di erence of the gradients is also estimated.