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Title: Existence and regularity of minimizers for nonlocal energy functionals
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.  more » « less
Award ID(s):
1716790
PAR ID:
10101514
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Differential and integral equations
Volume:
31
Issue:
11/12
ISSN:
0893-4983
Page Range / eLocation ID:
807-832
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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