Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials

2025/05/26 by De Pas, Francesco, Dipierro, Serena, Piccinini, Mirco +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.20054

Abstract

We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type (1)/(4)\iint_{ℝ²ⁿ∖ (ℝⁿ ∖ Ω)²}|u(x)-u(y)|² K(x-y) dx dy + ∫_ΩW(u(x)) dx. Here, W is a possibly degenerate double well potential with a polynomial control on its second derivative near the wells. Also, K belongs to a wide class of measurable kernels and is modeled on that of the fractional Laplacian.

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Cited by

• A further remark on the density estimate for degenerate Allen-Cahn equations: Δ_p-type equations for 1

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