277 citations · 895 across the 70 of their papers we have counts for
68 papers · 1 filter
Symmetry of hypersurfaces and the Hopf Lemma
YanYan Li
A classical theorem of A.D. Alexandrov says that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere. We give exposition to som…
Gradient estimates for the insulated conductivity problem: the non-umbilical case
Hongjie Dong, Yanyan Li, Zhuolun Yang
We study the insulated conductivity problem with inclusions embedded in a bounded domain in , for . The gradient of solutions may blow up as , th…
Regularity of viscosity solutions of the -Loewner-Nirenberg problem
YanYan Li, Luc Nguyen, Jingang Xiong
We study the regularity of the viscosity solution of the -Loewner-Nirenberg problem on a bounded smooth domain for . It was known that $u…
Anisotropic Caffarelli-Kohn-Nirenberg type inequalities
YanYan Li, Xukai Yan
Caffarelli, Kohn and Nirenberg considered in 1984 the interpolation inequalities \[\||x|^{γ_1}u\|_{L^s(\mathbb{R}^n)}\le C\||x|^{γ_2}\nabla u\|_{L^p(\mathbb{R}^n)}^a\||x|^{γ_3}u\|_…
Optimal gradient estimates of solutions to the insulated conductivity problem in dimension greater than two
Hongjie Dong, YanYan Li, Zhuolun Yang
We study the insulated conductivity problem with inclusions embedded in a bounded domain in . The gradient of solutions may blow up as , the distance bet…
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…