A Type of Nonlocal Elliptic Problem: Existence and Approximation Through a Galerkin--Fourier Method

DOI10.1137/140963066zbMath1325.35025OpenAlexW2038849474MaRDI QIDQ5264958

Julio Muñoz, Fuensanta Andrés

Publication date: 21 July 2015

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

Full work available at URL: http://hdl.handle.net/10578/28067

zbMATH Keywords

nonlocalityvariational techniquesperidynamicsapproximation of partial differential equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Asymptotic theory of functional-differential equations (34K25) Methods involving semicontinuity and convergence; relaxation (49J45) Singular nonlinear integral equations (45G05)

Related Items (9)

Optimal design problems governed by the nonlocal \(p\)-Laplacian equation ⋮ A restricted nonlocal operator bridging together the Laplacian and the fractional Laplacian ⋮ The Galerkin-Fourier method for the study of nonlocal parabolic equations ⋮ Principal spectral theory of time‐periodic nonlocal dispersal operators of Neumann type ⋮ The Nonlocal Kelvin Principle and the Dual Approach to Nonlocal Control in the Conduction Coefficients ⋮ Nonlocal Basis Pursuit: Nonlocal Optimal Design of Conductive Domains in the Vanishing Material Limit ⋮ Nonlocal Control in the Conduction Coefficients: Well-Posedness and Convergence to the Local Limit ⋮ On the convergence of a class of nonlocal elliptic equations and related optimal design problems ⋮ Nonlocal optimal design: a new perspective about the approximation of solutions in optimal design

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