scholarly journals On the blow-up boundary solutions of the Monge -Ampére equation with singular weights

2012 ◽  
Vol 11 (2) ◽  
pp. 697-708 ◽  
Author(s):  
Haitao Yang ◽  
◽  
Yibin Chang
Keyword(s):  
Blow Up ◽  
Monge Ampere ◽  
Boundary Solutions ◽  
Singular Weights

Refined Boundary Behavior of the Unique Convex Solution to a Singular Dirichlet Problem for the Monge–Ampère Equation

2018 ◽  
Vol 18 (2) ◽  
pp. 289-302
Author(s):  
Zhijun Zhang
Keyword(s):  
Dirichlet Problem ◽  
Crucial Role ◽  
Blow Up ◽  
Boundary Behavior ◽  
Structure Condition ◽  
Bounded Smooth Domain ◽  
Convex Solution ◽  
Bounded Smooth ◽  
Monge Ampere ◽  
Singular Dirichlet Problem

AbstractThis paper is concerned with the boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge–Ampère equation\operatorname{det}D^{2}u=b(x)g(-u),\quad u<0,\,x\in\Omega,\qquad u|_{\partial% \Omega}=0,where Ω is a strictly convex and bounded smooth domain in{\mathbb{R}^{N}}, with{N\geq 2},{g\in C^{1}((0,\infty),(0,\infty))}is decreasing in{(0,\infty)}and satisfies{\lim_{s\rightarrow 0^{+}}g(s)=\infty}, and{b\in C^{\infty}(\Omega)}is positive in Ω, but may vanish or blow up on the boundary. We find a new structure condition ongwhich plays a crucial role in the boundary behavior of such solution.

scholarly journals Blow up boundary solutions of some semilinear fractional equations in the unit ball

2016 ◽  
Vol 140 ◽  
pp. 236-253 ◽  
Author(s):  
Mohamed Ben Chrouda ◽  
Mahmoud Ben Fredj
Keyword(s):  
Unit Ball ◽  
Blow Up ◽  
Fractional Equations ◽  
Boundary Solutions

Blow-up boundary solutions of semilinear elliptic problems

2002 ◽  
Vol 48 (4) ◽  
pp. 521-534 ◽  
Author(s):  
Florica Şt. Cı̂rstea ◽  
Vicentctiu D. Rǎdulescu
Keyword(s):  
Blow Up ◽  
Elliptic Problems ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Boundary Solutions
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