On the Existence of Solutions to the Monge-ampère Equation with Infinite Boundary Values
نویسندگان
چکیده
Given a positive and an increasing nonlinearity f that satisfies an appropriate growth condition at infinity, we provide a condition on g ∈ C∞(Ω) for which the Monge-Ampère equation detD2u = gf(u) admits a solution with infinite boundary value on a strictly convex domain Ω. Sufficient conditions for the nonexistence of such solutions will also be given.
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