68 citations · 234 across the 39 of their papers we have counts for
48 papers
Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization
Guoqing Cui, Chong Gu, Nam Q. Le +2
We establish interior and global Hölder estimates for linearized Monge-Ampère equations in divergence form in all dimensions , when the Hessian determinant of the convex M…
Unbounded variation solutions for uniformly elliptic equations in nondivergence form in dimension three
Nam Q. Le, Qi Sun, Hung V. Tran
For each nonnegative integer , we construct smooth symmetric coefficient matrices satisfying the fixed ellipticity bound \[ I\leq A_m\leq 2^{81}I \] for which…
A Green's function approach to linearized Monge-Ampère equations in divergence form and application to singular Abreu type equations
Chong Gu, Nam Q. Le
In this paper, we establish local and global regularity estimates for linearized Monge-Ampère equations in divergence form via critical Lorentz space estimates for the Green's func…
Curvature-informed multi-task learning for graph networks
Alexander New, Michael J. Pekala, Nam Q. Le +3
Properties of interest for crystals and molecules, such as band gap, elasticity, and solubility, are generally related to each other: they are governed by the same underlying laws…
Remarks on sharp boundary estimates for singular and degenerate Monge-Ampère equations
Nam Q. Le
By constructing appropriate smooth, possibly non-convex supersolutions, we establish sharp lower bounds near the boundary for the modulus of nontrivial solutions to singular and de…
Hadamard-type inequalities for -positive matrices
Nam Q. Le
We establish Hadamard-type inequalities for a class of symmetric matrices called -positive matrices for which the -th elementary symmetric functions of their eigenvalues are…