5 papers · 1 filter
A short note about the spaces
Guillermo García-Sáez
In this short communication we answer negatively to a question posed by the authors in their work \cite[Section 1.4]{Brue2022} about the complex interpolation nature of the spaces…
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…
Asymptotics of variational eigenvalues for a general nonlocal -Laplacian with varying horizon
Guillermo García-Sáez
From the recent developing of nonlocal gradients with finite horizon based on general kernels, we introduce a new nonlocal -Laplacian and study the eigenvalue problem asso…
Fractional weighted Sobolev spaces associated to the Riesz fractional gradient
Guillermo García-Sáez
In this work, we introduce a new family of functions spaces, the weighted fractional Sobolev spaces , where is a weight in the Muckenhoupt class . This s…