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math.AP2022★ 1 cited
Minimizers of Nonlocal Polyconvex Energies in Nonlocal Hyperelasticity
José C. Bellido, Javier Cueto, Carlos Mora-Corral
We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many f…
math.AP2022★ 3 cited
Nonlocal gradients in bounded domains motivated by Continuum Mechanics: Fundamental Theorem of Calculus and embeddings
José Carlos Bellido, Javier Cueto, Carlos Mora-Corral
In this paper we develop a new set of results based on a nonlocal gradient jointly inspired by the Riesz s-fractional gradient and Peridynamics, in the sense that its integration d…