Abstract
For all n⩾1, we are interested in bounded solutions of the Allen–Cahn equation Δu+u−u3=0 which are defined in all Rn+1 and whose zero set is asymptotic to a given minimal cone. In particular, in dimension n+1⩾8, we prove the existence of stable solutions of the Allen–Cahn equation whose zero sets are not hyperplanes.
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