Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium

Abstract

We consider a non-local phase transition equation set in a periodic medium and we construct solutions whose interface stays in a slab of prescribed direction and universal width. The solutions constructed also enjoy a local minimality property with respect to a suitable non-local energy functional.

References in corpus (4)

• Local behavior of fractional $p$-minimizers
• Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
• Regularity estimates for elliptic nonlocal operators
• Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces

Cited by in corpus (7)

• Nonlocal diffusion and applications
• Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
• One-dimensional solutions of non-local Allen-Cahn-type equations with rough kernels
• Planelike interfaces in long-range Ising models and connections with nonlocal minimal surfaces
• Nonlocal phase transitions in homogeneous and periodic media
• Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
• Minimizers for nonlocal perimeters of Minkowski type