The second expansion of the unique vanishing at infinity solution to a singular elliptic equation

Wan, Haitao; Shi, Yongxiu

doi:10.1016/j.na.2018.02.007

Nonlinear Analysis

2018

DOI: 10.1016/j.na.2018.02.007

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The second expansion of the unique vanishing at infinity solution to a singular elliptic equation

Haitao Wan

Yongxiu Shi

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2021

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Cited by 1 publication

References 40 publications

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Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation

Wan¹,

Shi²,

Liu³

2021

Advances in Nonlinear Analysis

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In this paper, we establish the second boundary behavior of the unique strictly convex solution to a singular Dirichlet problem for the Monge-Ampère equation det ( D 2 u ) = b ( x ) g ( − u ) , u < 0 in Ω and u = 0 on ∂ Ω , $$\mbox{ det}(D^{2} u)=b(x)g(-u),\,u<0 \mbox{ in }\Omega \mbox{ and } u=0 \mbox{ on }\partial\Omega, $$ where Ω is a bounded, smooth and strictly convex domain in ℝ N (N ≥ 2), b ∈ C∞(Ω) is positive and may be singular (including critical singular) or vanish on the boundary, g ∈ C 1((0, ∞), (0, ∞)) is decreasing on (0, ∞) with lim t → 0 + g ( t ) = ∞ $ \lim\limits_{t\rightarrow0^{+}}g(t)=\infty $ and g is normalized regularly varying at zero with index −γ(γ>1). Our results reveal the refined influence of the highest and the lowest values of the (N − 1)-th curvature on the second boundary behavior of the unique strictly convex solution to the problem.

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Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation

Wan¹,

Shi²,

Liu³

2021

Advances in Nonlinear Analysis

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show abstract

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The second expansion of the unique vanishing at infinity solution to a singular elliptic equation

Cited by 1 publication

References 40 publications

Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation

Refined second boundary behavior of the unique strictly convex solution to a singular Monge-Ampère equation

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