5 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…