3 papers
math.AP2026
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…
math.AP2026
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…
math.AP2026
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…