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

Precise blowup rate near the boundary of boundary blowup solutions to k-Hessian equation

“…For Laplace equation which corresponds to the special case k ¼ 1, further studies on the asymptotic behavior such as higher order boundary estimates have been developed, see [1-3, 5, 6, 27] for example. Recently, there are some results for k-Hessian equation in this direction (for example, [11,13,16,[39][40][41]), but it seems that the results for the asymptotic behavior which have been obtained for k-Hessian equation are of type In this paper, we shall obtain more precise blowup rate near oX of solutions to (1.1)-(1.2). Before stating our result, we recall the notion of k-convexity of a function.…”

Convex solutions of Monge-Ampère equations and systems: Existence, uniqueness and asymptotic behavior

“…For example, in [51], Trudinger and Wang pointed out that Monge-Ampère equation can describe re ector shape design, or Weingarten curvature. In recent years, increasing attention has been paid to the study of the Monge-Ampère equations by di erent methods (see [3,4,7,11,13,22,23,25,34,37,38,42,45,47,52,56,57,60]). In particular in [62], Zhang and Wang studied the following Monge-Ampère equation det D u = e −u in Ω, u = on ∂Ω,…”