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
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Proc. Amer. Math. Soc. 135 (2007), 141-149 Request permission

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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