28 citations · 58 across the 12 of their papers we have counts for
5 papers · 1 filter
On the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase
Siyuan Lu
In this paper, we solve the Dirichlet problem for Lagrangian phase equation with critical and supercritical phase. A crucial ingredient is the interior estimate. Our result i…
On the -Nirenberg problem on
YanYan Li, Han Lu, Siyuan Lu
We establish theorems on the existence and compactness of solutions to the -Nirenberg problem on the standard sphere . A first significant ingredient, a Liouville…
A Liouville theorem for Möbius invariant equations
YanYan Li, Han Lu, Siyuan Lu
In this paper we classify Möbius invariant differential operators of second order in two dimensional Euclidean space, and establish a Liouville type theorem for general Möbius inva…
Monge-Ampère equation with bounded periodic data
YanYan Li, Siyuan Lu
We consider the Monge-Ampère equation in , where is a positive bounded periodic function. We prove that must be the sum of a quadratic polynomi…
Existence and nonexistence to exterior Dirichlet problem For Monge-Ampère equation
Yanyan Li, Siyuan Lu
We consider the exterior Dirichlet problem for Monge-Ampère equation with prescribed asymptotic behavior. Based on earlier work by Caffarelli and the first named author, we complet…