Heteroclinic connections for nonlocal equations
Analysis of PDEs
2019-10-29 v3
Abstract
We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a renormalized energy functional, exploits a perturbation method of viscosity type and develops a free boundary theory for a double obstacle problem of mixed local and nonlocal type. The description of the stationary positions for the atom dislocation function in a perturbed crystal, as given by the Peierls-Nabarro model, is a particular case of the result presented.
Keywords
Cite
@article{arxiv.1711.01491,
title = {Heteroclinic connections for nonlocal equations},
author = {Serena Dipierro and Stefania Patrizi and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1711.01491},
year = {2019}
}