Existence and regularity of minimizers for nonlocal energy functionals

Mikil D. Foss; Petronela Radu; Cory Wright

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arXiv · 1902.01495

Existence and regularity of minimizers for nonlocal energy functionals

Mikil D. Foss·Petronela Radu·Cory Wright

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Abstract

In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. 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.

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Mikil D. Foss, Petronela Radu, Cory Wright. 2019-02-04. Existence and regularity of minimizers for nonlocal energy functionals. https://arxiv.org/abs/1902.01495

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