1d Symmetry for Semilinear Pdes from the Limit Interface of the Solution

Abstract

We study bounded, monotone solutions of ∆u = W ′(u) in the whole of R, where W is a double-well potential. We prove that under suitable assumptions on the limit interface and on the energy growth, u is 1D. In particular, differently from the previous literature, the solution is not assumed to have minimal properties and the cases studied lie outside the… (More)

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