Counterexamples to symmetry for partially overdetermined elliptic problems
Counterexamples to symmetry for partially overdetermined elliptic problems
We exhibit several counterexamples showing that the famous SerrinĀ“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 ā¦