Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings
From MaRDI portal
Publication:6075501
DOI10.1515/anona-2022-0316arXiv2201.08793OpenAlexW4385758417MaRDI QIDQ6075501
José Carlos Bellido, Carlos Mora-Corral, Javier Cueto
Publication date: 20 September 2023
Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.08793
peridynamicsnon-local gradientRiesz fractional gradientnon-local calculus of variationsnon-local embeddingsnon-local fundamental theorem of calculusnon-local Poincaré inequality
Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Fractional derivatives and integrals (26A33) Methods involving semicontinuity and convergence; relaxation (49J45) PDEs in connection with mechanics of deformable solids (35Q74) Optimality conditions for problems involving relations other than differential equations (49K21) Fractional partial differential equations (35R11) Peridynamics (74A70)
Related Items
Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups ⋮ Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications ⋮ Extending linear growth functionals to functions of bounded fractional variation
Cites Work
- Characterization of function spaces of vector fields and an application in nonlinear peridynamics
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
- Analysis of the volume-constrained peridynamic Navier equation of linear elasticity
- Nonlocal constrained value problems for a linear peridynamic Navier equation
- Localization of nonlocal gradients in various topologies
- A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
- An \(L^1\)-type estimate for Riesz potentials
- Variational theory and domain decomposition for nonlocal problems
- Force flux and the peridynamic stress tensor
- On a new class of fractional partial differential equations
- Hyperelasticity as a \(\Gamma\)-limit of peridynamics when the horizon goes to zero
- Functional analysis, Sobolev spaces and partial differential equations
- An estimate in the spirit of Poincaré's inequality
- Elliptic partial differential equations of second order
- Existence and regularity of minimizers for nonlocal energy functionals.
- On a new class of fractional partial differential equations. II
- Effect of surface slip on the relative motion and collision efficiency of slippery spherical particles
- Reformulation of elasticity theory for discontinuities and long-range forces
- Fractional vector analysis based on invariance requirements (critique of coordinate approaches)
- Getting acquainted with the fractional Laplacian
- Quasiconvexity in the fractional calculus of variations: characterization of lower semicontinuity and relaxation
- Towards a unified theory of fractional and nonlocal vector calculus
- Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
- Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions
- Fractional Piola identity and polyconvexity in fractional spaces
- Bond-based peridynamics does not converge to hyperelasticity as the horizon goes to zero
- \( \Gamma\)-convergence of polyconvex functionals involving \(s\)-fractional gradients to their local counterparts
- Dirichlet's principle and wellposedness of solutions for a nonlocal \(p\)-Laplacian system
- A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
- On nonlocal variational and quasi-variational inequalities with fractional gradient
- Peridynamic states and constitutive modeling
- A fractional Korn-type inequality
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity
- Peridynamic Theory and Its Applications
- NONLOCAL KORN-TYPE CHARACTERIZATION OF SOBOLEV VECTOR FIELDS
- Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
- Results on Nonlocal Boundary Value Problems
- A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems
- A Nonlocalp-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions
- On the variational limit of a class of nonlocal functionals related to peridynamics
- Variational Methods for Nonlocal Fractional Problems
- Classical Fourier Analysis
- Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling
- Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization
- Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications
- Peridynamics review
- A new theory of fractional differential calculus
- The Fractional Laplacian
- Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling
- From non-local Eringen’s model to fractional elasticity
- Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
- Existence for Nonlocal Variational Problems in Peridynamics
- An Extension Problem Related to the Fractional Laplacian
- Numerical methods for nonlocal and fractional models
- Direct methods in the calculus of variations
- Nonlocal equations in bounded domains: a survey
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
