8 papers
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…
Generalized Sobolev-Orlicz spaces based on the Riesz fractional gradient as interpolation and potential spaces
Pedro Miguel Campos, Guillermo García-Sáez
In this work we establish that the recently introduced fractional Sobolev spaces based on the Riesz fractional gradient of Musielak-Orlicz functions by one of the authors, coincide…
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…
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…