Calculus of Variations and Geometric Measure Theory
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I. FragalĂ  - F. Gazzola - J. Lamboley - M. Pierre

Counterexamples to Symmetry for Partially Overdetermined Elliptic Problems

created by lamboley on 21 May 2016


Published Paper

Inserted: 21 may 2016
Last Updated: 21 may 2016

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


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.


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