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math.AP2024
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}^…
math.AP2024
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 \mat…