14 citations · 38 across the 19 of their papers we have counts for
22 papers
Nonlocal gradient, the nonlocal Laplacian and maximum principles
José Carlos Bellido, Guillermo García-Sáez, José Camilo Rueda-Niño
We study the nonlocal -Laplacian, defined as the composition of the nonlocal divergence and gradient operators associated with a general radial kernel : $Δ_ρu=\mbox{div}_ρ\le…
A general theory of nonlocal elasticity based on nonlocal gradients and connections with Eringen's model
J. C. Bellido, G. García-Sáez
We develop a general theory of nonlocal linear elasticity based on nonlocal gradients with general radial kernels. Starting from a nonlocal hyperelastic energy functional, we perfo…
Compact embeddings of Bessel Potential Spaces
José C. Bellido, Javier Cueto, Guillermo García-Sáez
Bessel potential spaces have gained renewed interest due to their robust structural properties and applications in fractional partial differential equations (PDEs). These spaces, d…
Bessel Potential Spaces and Complex Interpolation: Continuous embeddings
José Carlos Bellido, Guillermo García-Sáez
Bessel potential spaces, introduced in the 1960s, are derived through complex interpolation between Lebesgue and Sobolev spaces, making them intermediate spaces of fractional diffe…
Nonlocal gradients: Fundamental theorem of calculus, Poincaré inequalities and embeddings
José Carlos Bellido, Carlos Mora-Corral, Hidde Schönberger
We address the study of nonlocal gradients defined through general radial kernels . Our investigation focuses on the properties of the associated function spaces, which depend o…
Nonlocal Green theorems and Helmholtz decompositions for truncated fractional gradients
José C. Bellido, Javier Cueto, Mikil Foss +1
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite suppor…