Existence and uniqueness theorems for singular anisotropic quasilinear elliptic boundary value problems
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- by S. Hill, K. S. Moore and W. Reichel PDF
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Abstract:
On bounded domains $\Omega \subset \mathbb {R}^2$ we consider the anisotropic problems $u^{-a}u_{xx}+u^{-b}u_{yy}=p(x,y)$ in $\Omega$ with $a,b>1$ and $u=\infty$ on $\partial \Omega$ and $u^cu_{xx}+u^du_{yy}+q(x,y)=0$ in $\Omega$ with $c,d\geq 0$ and $u=0$ on $\partial \Omega$. Moreover, we generalize these boundary value problems to space-dimensions $n>2$. Under geometric conditions on $\Omega$ and monotonicity assumption on $0<p,q\in \mathcal {C}^\alpha (\overline {\Omega })$ we prove existence and uniqueness of positive solutions.References
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Additional Information
- S. Hill
- Affiliation: Department of Mathematics, Rowan University, Glassboro, New Jersey 08028
- K. S. Moore
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Address at time of publication: Department of Mathematics, University of Michigan, 525 East University Ave., Ann Arbor, Michigan 48109-1109
- Email: ksmoore@math.lsa.umich.edu
- W. Reichel
- Affiliation: Mathematisches Institut, Universität zu Köln, 50931 Köln, Germany
- Address at time of publication: Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland
- Email: reichel@eichler.math-lab.unibas.ch
- Received by editor(s): July 9, 1998
- Published electronically: February 7, 2000
- Communicated by: Lesley M. Sibner
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1673-1683
- MSC (2000): Primary 35J65; Secondary 35J70
- DOI: https://doi.org/10.1090/S0002-9939-00-05493-9
- MathSciNet review: 1695131