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.
k-ended O(m)×O(n) invariant solutions to the Allen-Cahn equation with infinite Morse index
Rizzi M.
2022-01-01
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.File in questo prodotto:
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