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Creators/Authors contains: "Radu, Petronela"

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  1. ; ; (, Journal of Peridynamics and Nonlocal Modeling)
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  2. ; (, SN Partial Differential Equations and Applications)
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  3. ; ; ; (, Journal of Peridynamics and Nonlocal Modeling)
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  4. ; ; ; ; (, Journal of Peridynamics and Nonlocal Modeling)
    Nonlocal operators that have appeared in a variety of physical models satisfy identities and enjoy a range of properties similar to their classical counterparts. In this paper, we obtain Helmholtz-Hodge type decompositions for two-point vector fields in three components that have zero nonlocal curls, zero nonlocal divergence, and a third component which is (nonlocally) curl-free and divergence-free. The results obtained incorporate different nonlocal boundary conditions, thus being applicable in a variety of settings. 
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  5. ; ; (, Differential and integral equations)
    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. 
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