We construct new families of two-ended O(m) x O(n)-invariant solutions to the Allen-Cahn equation Delta u + u - u(3)=0 in RN+1, with N >= 7, whose zero level sets diverge logarithmically from the Lawson cone at infinity. The construction is based on a careful study of the Jacobi-To da system on a given O(m) x O(n)-invariant manifold, which is asymptotic to the Lawson cone at infinity.
Doubling construction for O(m)×O(n) invariant solutions to the Allen–Cahn equation
Rizzi M.
2022-01-01
Abstract
We construct new families of two-ended O(m) x O(n)-invariant solutions to the Allen-Cahn equation Delta u + u - u(3)=0 in RN+1, with N >= 7, whose zero level sets diverge logarithmically from the Lawson cone at infinity. The construction is based on a careful study of the Jacobi-To da system on a given O(m) x O(n)-invariant manifold, which is asymptotic to the Lawson cone at infinity.File in questo prodotto:
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