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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Given a positive and an increasing nonlinearity that satisfies an appropriate growth condition at infinity, we provide a condition on
for which the Monge-Ampère equation
admits a solution with infinite boundary value on a strictly convex domain
. 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.