Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization

DOI10.1137/16M1078811zbMath1373.46030MaRDI QIDQ5737799

Qiang Du, Xiaochuan Tian

Publication date: 30 May 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

trace mapHardy inequalitynonlocal operatornonlocal function spacevanishing horizonheterogeneous localization

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Regularity of solutions in optimal control (49N60) Integral operators (47G10) PDEs in connection with mechanics of deformable solids (35Q74) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (19)

Nonlocal trace spaces and extension results for nonlocal calculus ⋮ A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization ⋮ Numerical methods for nonlocal and fractional models ⋮ Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions ⋮ Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization ⋮ A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models ⋮ An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions ⋮ Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon ⋮ Quasi-nonlocal Coupling of Nonlocal Diffusions ⋮ Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations ⋮ Nonlocal Wave Propagation in Unbounded Multi-Scale Media ⋮ Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models ⋮ Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling ⋮ Reduction of integration domain in Triebel–Lizorkin spaces ⋮ Peridynamics boundary condition treatments via the pseudo-layer enrichment method and variable horizon approach ⋮ Function spaces and extension results for nonlocal Dirichlet problems ⋮ Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues ⋮ Traces on General Sets in ${R}^n$ for Functions with no Differentiability Requirements ⋮ Stability and error analysis for a second-order approximation of 1D nonlocal Schrödinger equation under DtN-type boundary conditions

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