Hopf ' S Lemma and Two Dimensional
نویسنده
چکیده
Let IR 2 be a bounded domain that is smooth except for a nite number of corners. The aim of this paper is to obtain conditions such that the solution of the Poisson problem ?u = f 0 in (f 6 = 0), with zero Dirichlet boundary condition, behaves similarly at the boundary as does the rst eigenfunction 1. That is: there exist c 1 ; c 2 > 0 such that c 1 1 (x) u (x) c 2 1 (x) : As a consequence we can improve some results for smooth domains to domains with corners, such as: the maximum principle for an equation with a potential which is unbounded near the boundary; the anti-maximum of Cl ement and Peletier; a Green function estimate of Zhao.
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