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Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case

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Abstract

This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampère equation detD2u(x) = b(x)f (u(x)), u > 0, x ∈ Ω, where Ω is a strictly convex and bounded smooth domain in ℝN with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b ∈ C∞ (Ω) is positive in Ω, but may be appropriate singular on the boundary.

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  1. School of Mathematics and Information Science, Yantai University, Yantai, 264005, P. R. China

    Zhi Jun Zhang

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  1. Zhi Jun Zhang
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Correspondence to Zhi Jun Zhang.

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This work are supported by NSF of P. R. China (Grant No. 11571295)

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Zhang, Z.J. Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case. Acta. Math. Sin.-English Ser. 35, 1190–1204 (2019). https://doi.org/10.1007/s10114-019-7524-4

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