David Gómez-Castro

activity

20172022

most citedThree representations of the fractional

p

-Laplacian: semigroup, extension and Balakrishnan formulas

30 citations · 98 across the 17 of their papers we have counts for

collaborators

Showing 2020Show all

5 papers · 1 filter

math.AP2020★ 30 cited

Three representations of the fractional $p$ -Laplacian: semigroup, extension and Balakrishnan formulas

Félix del Teso, David Gómez-Castro, Juan Luis Vázquez

We introduce three representation formulas for the fractional $p$ -Laplace operator in the whole range of parameters $0 < s < 1$ and $1 < p < \infty$ . Note that for $p \neq = 2$ this a nonlinea…

math.AP2020

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 $Ω$ of $R^{n}$ is the initial and boundary value problem. If the Laplace operator is replaced b…

math.AP2020★ 3 cited

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 $D^{s, p} (R^{n})$ and their embeddings, for $s \in (0, 1]$ and $p \geq 1$ . They are…

math.AP2020★ 1 cited

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 $[u]_{W^{s, p} (R^{n})}$ control translations. In particular, we prove that $\| u(\cdot + y) - u \|_{L^p (\ma…

math.AP2020★ 19 cited

Blow-up phenomena in nonlocal eigenvalue problems: when theories of $L^{1}$ and $L^{2}$ meet