On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems - Anoshchenko, O.; Lysenko, O.; Khruslov, E. (Журнал математической физики, анализа, геометрии, 2009)
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.