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arXiv · 2505.20054

Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials

Francesco De Pas·Serena Dipierro·Mirco Piccinini·Enrico Valdinoci
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Abstract

We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type $$ \frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\mathbb{R}^n \setminus \Omega)^2}|u(x)-u(y)|^2 K(x-y) \,dx dy + \int_\Omega W(u(x)) \,dx. $$ 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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Francesco De Pas, Serena Dipierro, Mirco Piccinini, Enrico Valdinoci. 2025-05-26. Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials. https://arxiv.org/abs/2505.20054

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