Proceedings of the American Mathematical Society

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

Author(s): Ahmed Mohammed
Journal: Proc. Amer. Math. Soc. 135 (2007), 141-149.
MSC (2000): Primary 35J65, 35J60, 35J25
Posted: June 20, 2006
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Abstract: Given a positive and an increasing nonlinearity

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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J65, 35J60, 35J25

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

DOI: 10.1090/S0002-9939-06-08623-0
PII: S 0002-9939(06)08623-0
Received by editor(s): July 25, 2005
Posted: June 20, 2006
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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