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On the existence of solutions to the Monge-Ampère equation with infinite boundary values


Author: Ahmed Mohammed
Journal: Proc. Amer. Math. Soc. 135 (2007), 141-149
MSC (2000): Primary 35J65, 35J60, 35J25
DOI: https://doi.org/10.1090/S0002-9939-06-08623-0
Published electronically: June 20, 2006
MathSciNet review: 2280183
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Abstract: Given a positive and an increasing nonlinearity $ f$ that satisfies an appropriate growth condition at infinity, we provide a condition on $ g\in C^\infty(\Omega)$ for which the Monge-Ampère equation $ \operatorname{det} D^2u=gf(u)$ admits a solution with infinite boundary value on a strictly convex domain $ \Omega$. Sufficient conditions for the nonexistence of such solutions will also be given.


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Additional Information

Ahmed Mohammed
Affiliation: Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306
Email: amohammed@bsu.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08623-0
Received by editor(s): July 25, 2005
Published electronically: June 20, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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