Published Paper

Inserted: 31 dec 2024
Last Updated: 1 jul 2025

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)
Year: 2025

Abstract:

We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non local energy functionals of the type \[ \frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\mathbb{R} \setminus \Omega)^2} (u(x)-u(y))^2 {K}(x-y) dx dy + \int_\Omega W(u(x)) dx. \] 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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