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Γ -convergence of polyconvex functionals involving s-fractional gradients to their local counterparts

Identificadores del recurso

Calculus of Variations and Partial Differential Equations 60.1 (2021): 7

0944-2669 (print)

1432-0835 (online)

http://hdl.handle.net/10486/700467

10.1007/s00526-020-01868-5

7-1

7-28

Procedència

(Biblos-e Archivo)

Fitxa

Títol:: Γ -convergence of polyconvex functionals involving s-fractional gradients to their local counterparts
Tema:: Nonlocal Diffusion; Dynamic Fracture; Crack Propagation; Riesz fractional gradient; Localization of nonlocal gradient; Bessel spaces; Polyconvex functionals; Matemáticas
Descripció:: This is a post-peer-review, pre-copyedit version of an article published in Calculus of Variations and Partial Differential Equations. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00526-020-01868-5; In this paper we study localization properties of the Riesz s-fractional gradient Dsu of a vectorial function u as s ↗ 1. The natural space to work with s-fractional gradients is the Bessel space Hs,p for 0 < s < 1 and 1 < p < ∞. This space converges, in a precise sense, to the Sobolev space W1,p when s ↗ 1. We prove that the s-fractional gradient Dsu of a function u in W1,p converges strongly to the classical gradient Du. We also show a weak compactness result in W1,p for sequences of functions us with bounded Lp norm of Dsus as s ↗ 1. Moreover, the weak convergence of Dsus in Lp implies the weak continuity of its minors, which allows us to prove a semicontinuity result of polyconvex functionals involving s-fractional gradients defined in Hs,p to their local counterparts defined in W1,p. The full -convergence of the functionals is achieved only for the case p > n; This work has been supported by the Agencia Estatal de Investigación of the Spanish Ministry Research and Innovation, through projects MTM2017-83740-P (J.C.B. and J.C.), and MTM2017-85934-C3-2-P (C.M.-C.)
Idioma:: English
Relació:: Gobierno de España. MTM2017-83740-P; Gobierno de España. MTM2017-85934-C3-2-P
Autor/Productor:: Bellido, José C.; Cueto, Javier; Mora Corral, Carlos
Editor:: Springer
Otros colaboradores/productores:: UAM. Departamento de Matemáticas
Drets:: open access
Data:: 2020-11-24
Tipo de recurso:: journal article; info:eu-repo/semantics/acceptedVersion
Format:: application/pdf

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