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Second order estimates on transition layers for the Allen-Cahn equation with homogeneous Neumann boundary conditions: Part I - Boundary-orthogonal transition layers
Akashdeep Dey, Wenkui Du, Davide Parise +1
We study stable solutions of the Allen-Cahn equation with homogeneous Neumann boundary condition on Riemannian manifolds with boundary in the regime where the transition layers mee…
Flat level sets of Allen-Cahn equation in half-space
Wenkui Du, Ling Wang, Yang Yang
We prove a half-space Bernstein theorem for Allen-Cahn equation. More precisely, we show that every solution of the Allen-Cahn equation in the half-space $\overline{\mathbb{R}^…
A half-space Bernstein theorem for anisotropic minimal graphs
Wenkui Du, Connor Mooney, Yang Yang +1
We prove that an anisotropic minimal graph over a half-space with flat boundary must itself be flat. This generalizes a result of Edelen-Wang to the anisotropic case. The proof use…
Flatness of anisotropic minimal graphs in
Wenkui Du, Yang Yang
We prove a Bernstein theorem for -anisotropic minimal hypersurfaces in all dimensional Euclidean spaces that the only entire smooth solutions $u: \mathbb{R}^{n}\rightarrow \math…