Counterexamples to Symmetry for Partially Overdetermined Elliptic Problems
Optimization and Control
2009-02-18 v1 Analysis of PDEs
Abstract
We exhibit several counterexamples showing that the famous Serrin's symmetry result for semilinear elliptic overdetermined problems may not hold for partially overdetermined problems, that is when both Dirichlet and Neumann boundary conditions are prescribed only 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.
Cite
@article{arxiv.0902.2947,
title = {Counterexamples to Symmetry for Partially Overdetermined Elliptic Problems},
author = {Ilaria Fragalà and Filippo Gazzola and Jimmy Lamboley and Michel Pierre},
journal= {arXiv preprint arXiv:0902.2947},
year = {2009}
}