70 citations · 313 across the 31 of their papers we have counts for
7 papers · 1 filter
The fractional p-Laplacian evolution equation in in the sublinear case
Juan Luis Vázquez
We consider the natural time-dependent fractional -Laplacian equation posed in the whole Euclidean space, with parameter and fractional exponent . Rather sta…
Three representations of the fractional -Laplacian: semigroup, extension and Balakrishnan formulas
Félix del Teso, David Gómez-Castro, Juan Luis Vázquez
We introduce three representation formulas for the fractional -Laplace operator in the whole range of parameters and . Note that for this a nonlinea…
Singular solutions for fractional parabolic boundary value problems
Hardy Chan, David Gómez-Castro, Juan Luis Vázquez
The standard problem for the classical heat equation posed in a bounded domain of is the initial and boundary value problem. If the Laplace operator is replaced b…
Characterisation of homogeneous fractional Sobolev spaces
Lorenzo Brasco, David Gómez-Castro, Juan Luis Vázquez
Our aim is to characterize the homogeneous fractional Sobolev-Slobodecki\uı spaces and their embeddings, for and . They are…
The evolution fractional p-Laplacian equation in . Fundamental solution and asymptotic behaviour
Juan Luis Vázquez
We consider the natural time-dependent fractional -Laplacian equation posed in the whole Euclidean space, with parameters and (fractional exponent). We show t…
Estimates on translations and Taylor expansions in fractional Sobolev spaces
Félix del Teso, David Gómez-Castro, Juan Luis Vázquez
In this paper we study how the (normalised) Gagliardo semi-norms control translations. In particular, we prove that $\| u(\cdot + y) - u \|_{L^p (\ma…