Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/3341

 Title: Local Overdetermined Linear Elliptic Problems in Lipschitz Domains with Solutions Changing Sign Authors: Canuto, BrunoRial, Diego Keywords: Overdetermined Boundary Value ProblemElliptic EquationRadial Symmetry Issue Date: 2009 Publisher: EUT - Edizioni Università di Trieste Citation: Bruno Canuto, Diego Rial, "Local Overdetermined Linear Elliptic Problems in Lipschitz Domains with Solutions Changing Sign", in Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 40 (2008), pp. 1-27. Series/Report no.: Rendiconti dell'Istituto di Matematica dell'Università di Trieste. An International Journal of Mathematics40 (2008) Abstract: We prove that the only domain $\Omega$ such that there exists a solution to the following overdetermined problem $\Deltau+\omega2u=−1$ in in $\Omega$, u = 0 on $\partial\Omega$, and $\partialnu = c$ on $\partial\Omega$, is the ball B1, independently on the sign of u, if we assume that the boundary $\partial\Omega$ is a perturbation (no necessarily regular) of the unit sphere $\partialB1$ of Rn. Here $\omega2 \neq (\lambdan)n\geq1$ (the eigenvalues of $−\Delta$ in B1 with Dirichlet boundary conditions), and $\omega \Lambda$, where $\Lambda$ is a enumerable set of R+, whose limit points are the values $\lambda1m$, for some integer $m\geq1$, $\lambda1m$ being the mth-zero of the first-order Bessel function I1. Description: pp.1-27 URI: http://hdl.handle.net/10077/3341 ISSN: 00494704 MS Classification 2000: 31B2035J25 Appears in Collections: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.40 (2008)

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