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A Singular Quasilinear Anisotropic Elliptic Boundary Value Problem. II

Authors:	Y S Choi P J McKenna

Institution:	Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268 ; Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268

Abstract:	Let $\Omega \subset \mathbf{R}^N$ with $N \geq 2$ . We consider the equations $\begin{displaymath}\begin{array}{rcl} \displaystyle \sum _{i=1}^{N} u^{a_i} \frac{\partial^2 u}{\partial x_i^2} +p(\mathbf{x})& = & 0, u\|_{\partial\Omega} & = & 0, \end{array} \end{displaymath}$ with $a_1 \geq a_2 \geq .... \geq a_N \geq 0$ and . We show that if $\Omega$ is a convex bounded region in $\mathbf{R}^N$ , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for non-convex domains in $\mathbf{R}^2$ are also given.

Keywords:	Harnack inequality singular subsolution supersolution

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