70 citations · 313 across the 31 of their papers we have counts for
40 papers
Remembering Louis Nirenberg and his mathematics
Juan Luis Vázquez
The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblemat…
Infinite-time concentration in Aggregation--Diffusion equations with a given potential
Jose A. Carrillo, David Gómez-Castro, Juan Luis Vázquez
Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assu…
Growing Solutions of the fractional -Laplacian equation in the Fast Diffusion Range
Juan Luis Vázquez
We establish existence, uniqueness as well as quantitative estimates for solutions to the fractional nonlinear diffusion equation, , where $…
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…