Existing and Regularity of Minimizers for Nonlocal Energy Functionals

Authors

Mikil D. Foss, University of Nebraska-LincolnFollow
Petronela Radu, University of Nebraska - LincolnFollow
Cory Wright, University of Nebraska-Lincoln

Date of this Version

1-2018

Citation

2018 Authors

Comments

Differential and Integral Equations Volume 31, Numbers 11-12 (2018), 807-832

Abstract

In this paper, we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics [19] or nonlocal diffusion models [1]. We derive nonlocal versions of the Euler-Lagrange equations under two sets of growth assumptions for the integrand. Existence of minimizers is shown for integrands with joint convexity (in the function and nonlocal gradient components). By using the convolution structure, we show regularity of solutions for certain Euler-Lagrange equations. No growth assumptions are needed for the existence and regularity of minimizers results, in contrast with the classical theory.