On the existence of solutions to the Monge-Ampère equation with infinite boundary values
By Ahmed Mohammed. 2006
49 citations recorded by the source corpus.
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-Ampere equation det D 2 u = g f(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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0e6372bf807cf2bef0e0436a53601c4a4ed83a1b
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Boundary behavior of large solutions to the Monge-Ampère equations with weights (2015, result): “1 in [35], and Theorem 1.”