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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, Bruno
Rial, Diego
Keywords: Overdetermined Boundary Value Problem
Elliptic Equation
Radial 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 Mathematics
40 (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: 31B20
35J25
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.40 (2008)

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