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On an overdetermined elliptic problem

Abstract : A smooth flat Riemannian manifold is called an exceptional domain if it admits positive harmonic functions having vanishing Dirichlet boundary data and constant (nonzero) Neumann boundary data. In analogy with minimal surfaces, a representation formula is derived and applied to the classification of exceptional domains. Some interesting open problems are proposed along the way.
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Submitted on : Wednesday, August 14, 2013 - 11:47:29 PM
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  • HAL Id : hal-00851578, version 1


Frank Pacard, Frédéric Hélein, Laurent Hauswirth. On an overdetermined elliptic problem. Pacific Journal of Mathematics, 2011, 250 (2), pp.319-334. ⟨hal-00851578⟩



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