Department of Mathematics, University of Zagreb, Bijenička cesta 30, HR-10000 Zagreb, Croatia

*e-mail:* `emarusic@math.hr`

**Abstract.** 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.

**2010 Mathematics Subject Classification.**
76D05, 76D07, 35B40, 35J05, 35Q30.

**Key words and phrases.** Boundary perturbation, asymptotic expansion, fluid flow,
Poisson equation, Poiseuille flow.

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