On Convergence of Solutions of Singularly Perturbed Boundary-Value Problems - Anoshchenko, O.; Lysenko, O.; Khruslov, E. (Журнал математичної фізики, аналізу, геометрії, 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 $L_1(Ω)$ as $ε→ 0$. The difference of the gradients is also estimated. Mathematics Subject Classification: 35B25, 35J05, 35J75, 35J40.