Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On a singular quasilinear anisotropic elliptic boundary value problem

Authors: Y. S. Choi, A. C. Lazer and P. J. McKenna
Journal: Trans. Amer. Math. Soc. 347 (1995), 2633-2641
MSC: Primary 35J65; Secondary 35J70
MathSciNet review: 1277103
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Abstract: We consider the problem

$\displaystyle {u^a}{u_{xx}} + {u^b}{u_{yy}} + p({\mathbf{x}}) = 0$

with $ a \geqslant 0$, $ b \geqslant 0$, on a smooth convex bounded region in $ {{\mathbf{R}}^2}$ with Dirichlet boundary conditions. We show that if the positive function $ p$ is uniformly bounded away from zero, then the problem has a classical solution.

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Keywords: Subsolution, supersolution, singular
Article copyright: © Copyright 1995 American Mathematical Society