A Singular Quasilinear Anisotropic Elliptic Boundary Value Problem. II
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- by Y. S. Choi and P. J. McKenna PDF
- Trans. Amer. Math. Soc. 350 (1998), 2925-2937 Request permission
Abstract:
Let $\Omega \subset \mathbf {R}^N$ with $N \geq 2$. We consider the equations \begin{align*} \sum _{i=1}^{N} u^{a_i} \frac {\partial ^2 u}{\partial x_i^2} +p(\mathbf {x})&= 0,\\ u|_{\partial \Omega } & = 0, \end{align*} with $a_1 \geq a_2 \geq \dots \geq a_N \geq 0$ and $a_1>a_N$. 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.References
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Additional Information
- Y. S. Choi
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
- Email: choi@math.uconn.edu
- P. J. McKenna
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
- Email: mckenna@math.uconn.edu
- Received by editor(s): August 6, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 2925-2937
- MSC (1991): Primary 35J25
- DOI: https://doi.org/10.1090/S0002-9947-98-02276-4
- MathSciNet review: 1491858