Interior regularity of the degenerate Monge-Ampère equation
2003 ◽
Vol 68
(1)
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pp. 81-92
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We study interior C1,1 regularity of generalised solutions of the Monge-Ampére equation det D2u = ψ, ψ ≥ 0, on a bounded convex domain Ω in ℝn with u = ϕ on ∂Ω. We prove in particular that u ∈ C1,1(Ω) if either i) ϕ = 0 and ψ1/(n − 1) ∈ C1,1 (Ω) or ii) Ω is C1,1 strongly convex, ϕ ∈ C1,1 (Ω̅), ψ1/(n − 1) ∈ C1,1(Ω̅) and ψ > 0 on U ∩ Ω, where U is a neighbourhood of ∂Ω. The main tool is an improvement of Pogorelov's well known C1,1 estimate so that it can be applied to the degenerate case.
2008 ◽
Vol 255
(7)
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pp. 1713-1723
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1985 ◽
Vol 08
(1)
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pp. 49-79
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2017 ◽
Vol 311
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pp. 306-313
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1985 ◽
Vol 31
(2)
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pp. 181-184
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Keyword(s):