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VOL. 85 | 2020 Simons cone and saddle solutions of the Allen-Cahn equation
Kelei Wang

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

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

Rights: Copyright © 2020 Mathematical Society of Japan

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