Boundary perturbation for the Dirichlet boundary value problem

Sa？etak We study the effects of small boundary perturbations on the solutions of the boundary value problems posed in such domains. We start from the domain Ω and then perturb its boundary by the product of a small parameter and some smooth function. The zeroth order approximation is simply the same boundary value problem posed in domain Ω, but the first order corrector is also found, containing some interesting effects