Journal article

Publication year: 2022

Journal: Journal of Functional Analysis

Volume number: 283

Issue number: 5

ISSN: 0022-1236

eISSN: 1096-0783

DOI Link: https://doi.org/10.1016/j.jfa.2022.109561

Publisher: Elsevier

Abstract: 
In this work we study existence, asymptotic behaviour and stability properties of O(m) x O(n)-invariant solutions of the Allen-Cahn equation Delta u + u(1 - u(2)) = 0 in R-m x R-n with m, n >= 2 and m + n >= 8. We exhibit four families of solutions whose nodal sets are smooth logarithmic corrections of the Lawson cone and with infinite Morse index. This work complements the study started in [23] by Pacard and Wei and [1] by Agudelo, Kowalczyk and Rizzi. (C) 2022 Elsevier Inc. All rights reserved.

Harvard Citation style: Agudelo, O. and Rizzi, M. (2022) k-ended O(m) x O(n) invariant solutions to the Allen-Cahn equation with infinite Morse index, Journal of Functional Analysis, 283(5), Article 109561. https://doi.org/10.1016/j.jfa.2022.109561

APA Citation style: Agudelo, O., & Rizzi, M. (2022). k-ended O(m) x O(n) invariant solutions to the Allen-Cahn equation with infinite Morse index. Journal of Functional Analysis. 283(5), Article 109561. https://doi.org/10.1016/j.jfa.2022.109561