Fractional Piola identity and polyconvexity in fractional spaces

DOI10.1016/j.anihpc.2020.02.006zbMath1442.35445arXiv1812.05848OpenAlexW3011643437MaRDI QIDQ2188113

Carlos Mora-Corral, Javier Cueto, José Carlos Bellido

Publication date: 3 June 2020

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.05848

zbMATH Keywords

polyconvexitynonlocal variational problemsRiesz fractional gradientfractional Piola identity

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Variational methods applied to PDEs (35A15) Fractional derivatives and integrals (26A33) Methods involving semicontinuity and convergence; relaxation (49J45) Elastic materials (74B99) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11)

Related Items (14)

Leibniz rules and Gauss-Green formulas in distributional fractional spaces ⋮ A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics~II ⋮ Failure of the local chain rule for the fractional variation ⋮ Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings ⋮ A sufficient condition for the lower semicontinuity of nonlocal supremal functionals in the vectorial case ⋮ Extending linear growth functionals to functions of bounded fractional variation ⋮ On a special class of non-local variational problems ⋮ \( \Gamma\)-convergence of polyconvex functionals involving \(s\)-fractional gradients to their local counterparts ⋮ A simple characterization of \(H\)-convergence for a class of nonlocal problems ⋮ Quasiconvexity in the fractional calculus of variations: characterization of lower semicontinuity and relaxation ⋮ On non-locality in the calculus of variations ⋮ Cartesian convexity as the key notion in the variational existence theory for nonlocal supremal functionals ⋮ Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition ⋮ The fractional variation and the precise representative of \(BV^{\alpha,p}\) functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Characterization of function spaces of vector fields and an application in nonlinear peridynamics
• Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
• Localization of nonlocal gradients in various topologies
• An \(L^1\)-type estimate for Riesz potentials
• Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity
• On a new class of fractional partial differential equations
• Linearized theory of peridynamic states
• Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• Convexity conditions and existence theorems in nonlinear elasticity
• On a new class of fractional partial differential equations. II
• Solvability of nonlocal systems related to peridynamics
• Quasistatic crack growth in nonlinear elasticity
• An existence theory for nonlinear elasticity that allows for cavitation
• A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
• The Dirichlet problem for nonlocal operators
• A fractional Korn-type inequality
• On the thermodynamics of system with nonlocality
• Nonlocal continuum mechanics
• Some Open Problems in Elasticity
• On the variational limit of a class of nonlocal functionals related to peridynamics
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics
• THE SOBOLEV NORM OF CHARACTERISTIC FUNCTIONS WITH APPLICATIONS TO THE CALDERON INVERSE PROBLEM
• From non-local Eringen’s model to fractional elasticity
• Sobolev Spaces
• Direct methods in the calculus of variations
• Nonlocal equations in bounded domains: a survey

This page was built for publication: Fractional Piola identity and polyconvexity in fractional spaces