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Equadiff 2003 - International Conference on Differential Equations
July 22-26, 2003
LUC Diepenbeek
Hasselt, Belgium

Organizers
Freddy Dumortier (Chair, LUC Diepenbeek), Henk Broer (Univ. Groningen), Jean-Pierre Gossez (Univ. Libre Bruxelles), Jean Mawhin (Univ. Cath. Louvain-la-Neuve), Andre Vanderbauwhede (Univ. Gent), Sjoerd Verduyn Lunel (Univ. Leiden)

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Elliptic boundary value problems in varying domains
by
Marius Bochniak
Abteilung Analysis, Universitaet Ulm, Helmholtzstr. 18, 89069 Ulm, Germany

We cinsider the Dirichlet problem for a fully nonlinear elliptic equation
F(x, u, Du, D2 u) = 0 in \Omega\epsilon,     u = 0 on \partial\Omega\epsilon,
where { \Omega\epsilon: | \epsilon| <= \epsilon0 } is a family of bounded domains in Rn, n >= 2 depending on a small parameter \epsilon and is defined by
\Omega\epsilon = \Phi\epsilon (\Omega), \partial \Omega\epsilon = \Phi\epsilon (\partial\Omega)
with \Phi\epsilon = I + \epsilon\Phi being a C\infty diffeomorphiosm.
Our goal is to find necessary and sufficient conditions for the domain \Omega to be a birfurcation domain, i.e. for the existence of nontrivial solutions in \Omega\epsilon branching from the trivial solution in \Omega.

Date received: May 30, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-34.