## M. Amar - L. R. Berrone - R. Gianni

# Asymptotic expansion for membranes subjected to a lifting force in a part of their boundary

created on 07 Jan 2002

modified on 16 Apr 2004

[

BibTeX]

*Published Paper*

**Inserted:** 7 jan 2002

**Last Updated:** 16 apr 2004

**Journal:** Asymptotic Analysis

**Volume:** 36

**Pages:** 319-343

**Year:** 2003

**Abstract:**

The framework of this paper is given by the mixed boundary-value problem
\[
\left

\begin{array}{lll}
\Delta u(x)=0, & & x\in \Omega
u(x)=0, & & x\in \Gamma _{0}
{\partial u\over\partial n}(x)=q(x), & & x\in \Gamma _{1}
\end{array}
\right.
\]
where $\Omega $ is a plane domain bounded by a regular curve composed by two
arcs $\Gamma _{0}$ and $\Gamma _{1}$. Assuming that $\left

\Gamma
_{1}\right

=\varepsilon $ and denoting by $u[\varepsilon ]$ the solution to
this problem, we study some asymptotic expansions in terms of $\varepsilon $
which are related to $u[\varepsilon ]$. Some connections are presented among
these expansions, on one hand, and the geometry of the domain $\Omega $, on
the other. In addition, a systematic way is found for computing at the
boundary the Ghizzetti's integral that solves the problem.