# Counterexamples to Symmetry for Partially Overdetermined Elliptic Problems

created by lamboley on 21 May 2016

[BibTeX]

Published Paper

Inserted: 21 may 2016
Last Updated: 21 may 2016

Journal: Analysis (Munich)
Volume: 29
Number: 1
Pages: 85-93
Year: 2009

Abstract:

We exhibit several counterexamples showing that the famous Serrin's symmetry result for semilinear elliptic overdetermined problems may not hold for {\em partially} overdetermined problems, that is when both Dirichlet and Neumann boundary conditions are prescribed only {\em on part} of the boundary. Our counterexamples enlighten subsequent positive symmetry results obtained by the first two authors for such partially overdetermined systems and justify their assumptions as well.