3 citations · 6 across the 10 of their papers we have counts for
11 papers
Localization for nonlocal gradient-based optimal control problems
Javier Cueto, Joshua M. Siktar
In this paper we consider optimal control problems in the nonlocal function space framework of Bellido-2023, where there are two different parameters: a horizon parameter ; a…
Compact embeddings of Bessel Potential Spaces
José C. Bellido, Javier Cueto, Guillermo García-Sáez
Bessel potential spaces have gained renewed interest due to their robust structural properties and applications in fractional partial differential equations (PDEs). These spaces, d…
-convergence involving nonlocal gradients with varying horizon: Recovery of local and fractional models
Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
This work revolves around the rigorous asymptotic analysis of models in nonlocal hyperelasticity. The corresponding variational problems involve integral functionals depending on n…
Nonlocal Green theorems and Helmholtz decompositions for truncated fractional gradients
José C. Bellido, Javier Cueto, Mikil Foss +1
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite suppor…
Eringen's model via linearization of nonlocal hyperelasticity
J. C. Bellido, J. Cueto, C. Mora-Corral
We consider Riesz' fractional gradient and a truncated version of it. The equations of nonlocal nonlinear elasticity based on those gradients are known. We perform a formal lineari…
A variational theory for integral functionals involving finite-horizon fractional gradients
Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the R…
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…
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…
-convergence of polyconvex functionals involving s-fractional gradients to their local counterparts
José C. Bellido, Javier Cueto, Carlos Mora-Corral
In this paper we study localization properties of the Riesz -fractional gradient of a vectorial function as . The natural space to work with -fracti…
Bond-based peridynamics does not converge to hyperelasticity as the horizon goes to zero
J. C. Bellido, J. Cueto, C. Mora-Corral
Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in t…
Fractional Piola identity and polyconvexity in fractional spaces
José C. Bellido, Javier Cueto, Carlos Mora-Corral
In this paper we address nonlocal vector variational principles obtained by substitution of the classical gradient by the Riesz fractional gradient. We show the existence of minimi…