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

Mohammed, Ahmed

doi:10.1090/S0002-9939-06-08623-0

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 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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