10 citations · 24 across the 9 of their papers we have counts for
5 papers · 1 filter
On optimal Hölder regularity of solutions to the equation in two dimensions
Nam Q. Le
We show that for an drift in two dimensions, if the Hardy norm of is small, then the weak solutions to have the same optimal Hölder r…
solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations
Nam Q. Le
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudi…
On the second inner variations of Allen-Cahn type energies and applications to local minimizers
Nam Q. Le
In this paper, we obtain an explicit formula for the discrepancy between the limit of the second inner variations of -Laplace Allen-Cahn energies and the second inner variation…
Geometric properties of boundary sections of solutions to the Monge--Ampère equation and applications
Nam Q. Le, Truyen Nguyen
In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge-Ampère equations: the engulfing and separating properties and volume…
On the second inner variation of the Allen-Cahn Functional and its applications
Nam Q. Le
In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Ca…