Sharp conditions for the existence of boundary blow-up solutions to the Monge–Ampère equation

Author(s)
Zhang, Xuemei
Du, Yihong
Publication Date
2018
Abstract
In this paper we give sharp conditions on K(x) and f (u) for the existence of strictly convex solutions to the boundary blow-up Monge-Ampère problem M[u](x) = K(x) f (u) for x ∈ Ω, u(x)→+∞ as dist(x, ∂Ω) → 0. Here M[u] = det (uxi x j ) is the Monge-Ampère operator, and Ω is a smooth, bounded, strictly convex domain in RN (N ≥ 2). Further results are obtained for the special case that Ω is a ball. Our approach is largely based on the construction of suitable sub- and super-solutions.
Citation
Calculus of Variations and Partial Differential Equations, 57(2), p. 1-24
ISSN
1432-0835
0944-2669
Link
https://hdl.handle.net/1959.11/23044
Language
en
Publisher
Springer
Title
Sharp conditions for the existence of boundary blow-up solutions to the Monge–Ampère equation
Type of document
Journal Article
Entity Type
Publication

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