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Counterexamples to symmetry for partially overdetermined elliptic problems
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Ilaria Fragalà
Published/Copyright:
September 25, 2009
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.
Published Online: 2009-09-25
Published in Print: 2009-04
© by Oldenbourg Wissenschaftsverlag, München, Germany
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Articles in the same Issue
- Restrictions of power series and functions to algebraic surfaces
- Approximate continuity and topological Boolean algebras
- A Tauberian theorem for absolute quasi-Nörlund means
- Boundary Nevanlinna–Pick interpolation for Nevanlinna matrix functions and the related Hamburger matrix moment problem
- Some new results on the semiduality of small sets of analytic functions
- A note on globally defined analytic sets
- Counterexamples to symmetry for partially overdetermined elliptic problems
- A uniqueness-type problem for linear iterative equations
- A new bound of Mason´s theorem
