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\title{Schwarz Alternating Methods for Eigenvalue and Nonlinear Problems}
\author{S.H. Lui\\
The Hong Kong Univ. of Science and Technology}
\date{}
\maketitle
The Schwarz Alternating Method was proposed by H. A. Schwarz more than
one hundred years ago to solve elliptic boundary value problems.  This
method has regained interest in recent years mainly because of its
potential as an efficient solution technique on modern parallel computers.
We first discuss a Schwarz Alternating Method for the eigenvalue problem
for the Laplacian operator, first developed by Maliassov.  We sketch 
a proof of the local convergence of this method.  It is shown that global 
convergence does not hold in general, except in the case of two 
overlapping subdomains. 

\vskip 2truemm 

In the second part, we discuss a Schwarz Alternating Method for a class of
semilinear elliptic equations whose nonlinearity satisfies a certainly Lipschitz
condition.  We sketch a proof of convergence of the Schwarz sequence.
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