A class of high order nonlocal operators

DOI10.1007/s00205-016-1025-8zbMath1362.46042OpenAlexW2467066737MaRDI QIDQ338121

Qiang Du, Xiaochuan Tian

Publication date: 4 November 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-016-1025-8

zbMATH Keywords

Sobolev inequalitiesnonlocal operatorshigh-order Sobolev spacesnonlocal function spacesnonlocal models of elastic beams and plates

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elasticity (74B20) Plates (74K20) Linear operators on function spaces (general) (47B38)

Related Items

Characterization of function spaces of vector fields and an application in nonlinear peridynamics ⋮ Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization ⋮ Positive powers of the Laplacian: from hypersingular integrals to boundary value problems ⋮ Quasi-nonlocal Coupling of Nonlocal Diffusions ⋮ Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization ⋮ A peridynamic model of fracture mechanics with bond-breaking

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Characterization of function spaces of vector fields and an application in nonlinear peridynamics
• Analysis of a scalar nonlocal peridynamic model with a sign changing kernel
• Hitchhiker's guide to the fractional Sobolev spaces
• Nonlocal constrained value problems for a linear peridynamic Navier equation
• Local integration by parts and Pohozaev identities for higher order fractional Laplacians
• Localization of nonlocal gradients in various topologies
• A nonlocal biharmonic operator and its connection with the classical analogue
• Image recovery via nonlocal operators
• Characterization of Sobolev and BV spaces
• Symmetric jump processes: localization, heat kernels and convergence
• An estimate in the spirit of Poincaré's inequality
• Reformulation of elasticity theory for discontinuities and long-range forces
• Random dispersal vs. non-local dispersal
• The Dirichlet problem for nonlocal operators
• Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems
• Nonlocal Operators with Applications to Image Processing
• Can the Nonlocal Characterization of Sobolev Spaces by Bourgain et al. Be Useful for Solving Variational Problems?
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
• Image Denoising Methods. A New Nonlocal Principle
• The bond-based peridynamic system with Dirichlet-type volume constraint
• An Extension Problem Related to the Fractional Laplacian
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• Nonlocal equations in bounded domains: a survey