Abstract
Simons cone is a minimal cone in $\mathbb{R}^8$, which provides a counterexample to the Bernstein problem. Corresponding objects for the Allen-Cahn equation are saddle solutions. They are conjectured to be minimal in dimension 8. We discuss some progress on this problem, in particular, the existence of minimizing solutions to Allen-Cahn equation in $\mathbb{R}^8$.
Information
Published: 1 January 2020
First available in Project Euclid: 29 December 2020
Digital Object Identifier: 10.2969/aspm/08510471
Subjects:
Primary:
35B33
,
35B40
,
35J20
,
35J25
Keywords:
Allen-Cahn equation
,
De Giorgi conjecture
,
global minimizer
,
Minimal cone
Rights: Copyright © 2020 Mathematical Society of Japan
