11 papers · 1 filter
Gradient rearrangement estimates for singular and degenerate anisotropic -Laplace equations
Lu Chen, Daniel Hauer, Yabo Yang
In this paper, we prove global pointwise estimates on the decreasing rearrangement \(u^{\ast}\) and \([H(\nabla u)]^{\ast}\) of SOLAs \(u\) of an elliptic Poisson equation driven b…
A -Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs
Lu Chen, Jiali Lan
We prove a Bernstein theorem for -anisotropic minimal hypersurfaces in dimensions that the only entire smooth solutions of -anisotropic minimal hypersurfa…
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…
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+\fra…
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…
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, a…
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}} { - Δu-\frac{1}{(1-|x|^2)^2} u = λe^u}, & {\rm in} \ \ B_1,\\ {\ \ \ \ u…
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 equation in the two-dimensional Poincaré disk : \begin{equ…
Classification of positive solutions of critical anisotropic Sobolev equation without the finite volume constraint
Lu Chen, Tian Wu, Jin Yan +1
In this paper, we classify all positive solutions of the critical anisotropic Sobolev equation \begin{equation}\label{0.1} -Δ^{H}_{p}u = u^{p^{*}-1}, \ \ x\in \mathbb{R}^n \end{equ…
Classification of positive solutions of Hardy-Sobolev equation without the finite volume constraints
Lu Chen, Yabo Yang
In this paper, we are concerned with the critical Hardy-Sobolev equation \begin{equation*} -Δ_{p}u = \frac{u^{p^{*}_s-1}}{|x|^{s}}, \ \ x\in \mathbb{R}^n \end{equation*} where $p^{…
Optimal concentration level of anisotropic Trudinger-Moser functionals on any bounded domain
Lu Chen, Rou Jiang, Maochun Zhu
Let be convex and homogeneous of degree , its polar represent a finsler metric on , and be any bounded open set in . In this pape…