Nonlocal Green theorems and Helmholtz decompositions for truncated fractional gradients
DOI10.1007/S00245-024-10160-3MaRDI QIDQ6589691
Javier Cueto, Mikil Foss, José Carlos Bellido, Petronela Radu
Publication date: 20 August 2024
Published in: Applied Mathematics and Optimization (Search for Journal in Brave)
fundamental solutionperidynamicsnonlocal vector calculusnonlocal gradientnonlocal Green identitiesnonlocal Helmholtz decomposition
Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Integral representations of solutions to PDEs (35C15) Integral operators (45P05) Integral operators (47G10) Approximation by operators (in particular, by integral operators) (41A35) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Linear integral equations (45A05) Integro-differential operators (47G20) Applications of functional analysis to differential and integral equations (46N20) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20)
Cites Work
- Title not available (Why is that?)
- Characterization of function spaces of vector fields and an application in nonlinear peridynamics
- Localization of nonlocal gradients in various topologies
- On a new class of fractional partial differential equations
- Some observations on the Green function for the ball in the fractional Laplace framework
- Linearized theory of peridynamic states
- On a new class of fractional partial differential equations. II
- Reformulation of elasticity theory for discontinuities and long-range forces
- Towards a unified theory of fractional and nonlocal vector calculus
- A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon
- Fractional Piola identity and polyconvexity in fractional spaces
- \( \Gamma\)-convergence of polyconvex functionals involving \(s\)-fractional gradients to their local counterparts
- A doubly nonlocal Laplace operator and its connection to the classical Laplacian
- A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up
- Nonlocal perimeter, curvature and minimal surfaces for measurable sets
- On the variational limit of a class of nonlocal functionals related to peridynamics
- Classical Fourier Analysis
- Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling
- Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements
- Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications
- Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings
- A variational theory for integral functionals involving finite-horizon fractional gradients
- Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity
Related Items (1)
This page was built for publication: Nonlocal Green theorems and Helmholtz decompositions for truncated fractional gradients
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6589691)
