Reproducing kernels of Sobolev–Slobodeckij˘ spaces via Green’s kernel approach: Theory and applications

DOI10.1142/s0219530523500112zbMath1529.41019OpenAlexW4380077318MaRDI QIDQ6166169

Hojatollah Adibi, Hamed Mohebalizadeh, Gregory E. Fasshauer

Publication date: 2 August 2023

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530523500112

zbMATH Keywords

eigenvalueself-adjoint operatorreproducing kerneleigenfunctioninterpolation spacepositive operatorfractional Laplacian operatorGreen's kernelcollocation meshless methodGalerkin meshless method

Mathematics Subject Classification ID

Numerical interpolation (65D05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Approximation by other special function classes (41A30) Spectral theory; eigenvalue problems on manifolds (58C40) Fractional partial differential equations (35R11) Spectral, collocation and related (meshless) methods applied to problems in statistical mechanics (82M22)

Related Items

Well-posedness of space fractional Ginzburg-Landau equations involving the fractional Laplacian arising in a Bose-Einstein condensation and its kernel based approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains
• Approximation of eigenfunctions in kernel-based spaces
• Mercer's theorem on general domains: on the interaction between measures, kernels, and RKHSs
• Local integration by parts and Pohozaev identities for higher order fractional Laplacians
• Mercer theorem for RKHS on noncompact sets
• Reproducing kernels of generalized Sobolev spaces via a Green function approach with distributional operators
• Progress on meshless methods. Invited papers based on the presentations at the 2nd ECCOMAS thematic conference on meshless methods, Porto, Portugal, July 9--11, 2007
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• Green function and Martin kernel for higher-order fractional Laplacians in balls
• A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
• Numerical approximation of the integral fractional Laplacian
• Reproducing kernels of Sobolev spaces via a Green kernel approach with differential operators and boundary operators
• Refined error estimates for Green kernel-based interpolation
• What is the fractional Laplacian? A comparative review with new results
• Fractional Laplace operator and Meijer G-function
• Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations
• Regularity of spectral fractional Dirichlet and Neumann problems
• Kernel-based Approximation Methods using MATLAB
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Integral representation of solutions to higher-order fractional Dirichlet problems on balls
• Interpolation Theory
• On the loss of maximum principles for higher-order fractional Laplacians
• A Unified Meshfree Pseudospectral Method for Solving Both Classical and Fractional PDEs
• Fixed Point Theorems and Applications
• Scattered Data Approximation
• On the fractional Laplacian of some positive definite kernels with applications in numerically solving the surface quasi-geostrophic equation as a prominent fractional calculus model
• Numerical methods for fractional diffusion