8 papers
Anisotropic minimal surface equation with Dirichlet boundary condition
Lu Chen, Jiali Lan, Haolin Liu
This paper investigates the Dirichlet problem for the anisotropic minimal surface equation in a bounded domain. Under the natural assumption of non-negative boundary anisotropic me…
The weighted isoperimetric inequality and Sobolev inequality outside convex sets
Lu Chen, Jiali Lan
In this paper, we establish a weighted capillary isoperimetric inequality outside convex sets using the -ABP method. The weight function is assumed to be positive, even,…
regularity of the Alt-Phillips Functional for negative powers
Lu Chen, Jiali Lan, Yong Wu
In this paper, we study the regularity of the free boundary for minimizers of the Alt-Phillips functional with negative powers \[\mathcal{E}_γ(u)=\int_Ω\frac{1}{2}|\nabla u|^2+\f…
Sharp capillary Sobolev inequality and Moser-Trudinger inequality outside convex domain
Lu Chen, Jiali Lan
The theory of sharp geometric inequality in and inside convex cone has been well-developed, much less known for sharp capillary geometric inequality outside convex d…
Quantitative properties of the Hardy-type mean field equation
Lu Chen, Bohan Wang, Chunhua Wang
In this paper, we consider the following Hardy-type mean field equation \[ \left\{ {\begin{array}{*{20}{c}} { - Îu-\frac{1}{(1-|x|^2)^2} u = λe^u}, & {\rm in} \ \ B_1,\\ {\ \ \ \…
Quantization analysis of Moser-Trudinger equations in the Poincaré disk and applications
Lu Chen, Qiaoqiao Hua, Guozhen Lu +2
In this paper, we first establish the quantitative properties for positive solutions to the Moser-Trudinger equations in the two-dimensional Poincaré disk : \begin{e…