Two-end solutions to the Allen-Cahn equation in R³
Gui, Changfeng · Liu, Yong · Wei, Juncheng
Original · EN
In this paper we consider the Allen-Cahn equation -Δu = u-u³ in R³ We prove that for each k∈(√2,+∞), there exists a solution to the equation which has growth rate k, i.e. u-H(· -k r + cₖ) ₗ∞ → 0 The main ingredients of our proof consist: (1) compactness of solutions with growth k, (2) moduli space theory of analytical variety of formal dimension one.
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