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November/December 2018 Existence and regularity of minimizers for nonlocal energy functionals
Mikil D. Foss, Petronela Radu, Cory Wright
Differential Integral Equations 31(11/12): 807-832 (November/December 2018).

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.

Citation

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Mikil D. Foss. Petronela Radu. Cory Wright. "Existence and regularity of minimizers for nonlocal energy functionals." Differential Integral Equations 31 (11/12) 807 - 832, November/December 2018.

Information

Published: November/December 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06986979
MathSciNet: MR3857865

Subjects:
Primary: 31B10, 34B10, 45G15, 49J99, 49K21, 49N60

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 11/12 • November/December 2018
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