61 citations · 118 across the 13 of their papers we have counts for
16 papers
On the nonlocal heat equation for certain Lévy operators and the uniqueness of positive solutions
Irene Gonzálvez, Fernando Quirós, Fernando Soria +1
We develop a Widder-type theory for nonlocal heat equations involving quite general Lévy operators. Thus, we consider nonnegative solutions and look for conditions on the operator…
Fractional KPZ equations with critical growth in the gradient respect to Hardy potential
Boumediene Abdellaoui, Ireneo Peral, Ana Primo +1
In this work we study the existence of positive solution to the fractional quasilinear problem, $$ \left\{ \begin{array}{rcll} (-Δ)^s u &=&λ\dfrac{u}{|x|^{2s}}+ |\nabla u|^{p}+ μf…
On the KPZ equation with fractional diffusion: global regularity and existence results
Boumediene Abdellaoui, Ireneo Peral, Ana Primo +1
In this work we analyze the existence of solutions to the fractional quasilinear problem, $$ (P) \left\{ \begin{array}{rcll} u_t+(-Δ)^s u &=&|\nabla u|^α+ f &\inn Ω_T\equivΩ\times…
Neumann conditions for the higher order -fractional Laplacian with
B. Barrios, L. Montoro, I. Peral +1
In this paper we study a variational Neumann problem for the higher order -fractional Laplacian, with . In the process, we introduce some non-local Neumann boundary conditi…
Principal Eigenvalue of Mixed Problem for the Fractional Laplacian: Moving the Boundary Conditions
Tommaso Leonori, Maria Medina, Ireneo Peral +2
We analyze the behavior of the eigenvalues of the following non local mixed problem $\left\{ \begin{array}{rcll} (-Δ)^{s} u &=& λ_1(D) \ u &\innΩ,\\ u&=&0&\inn D,\\ \mathcal{N}_{s}…
Regularity of solutions of the fractional porous medium flow with exponent 1/2
Luis Caffarelli, Juan Luis Vázquez
We study the regularity of a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. The precise model is $u_t=\nabla\cdot(u\nabla…
Muckenhoupt-Wheeden conjectures in higher dimensions
Alberto Criado, Fernando Soria
In recent work by Reguera and Thiele and by Reguera and Scurry, two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal funct…
On the dimension dependence of some weighted inequalities
Alberto Criado, Fernando Soria
In the context of radial weights we study the dimension dependence of some weighted inequalities for maximal operators. We study the growth of the -constants for radial weight…
A critical fractional equation with concave-convex power nonlinearities
B. Barrios, E. Colorado, R. Servadei +1
In this work we study the following fractional critical problem $$ (P_λ)=\left\{\begin{array}{ll} (-Δ)^s u=λu^{q} + u^{2^*_{s}-1}, \quad u{>}0 & \mbox{in} Ω\\ u=0 & \mbox{in} \RR^n…
Estimates for multiparameter maximal operators of Schrödinger type
Per Sjölin, Fernando Soria
Multiparameter maximal estimates are considered for operators of Schrödinger type. Sharp and almost sharp results, that extend work by Rogers and Villarroya, are obtained. We provi…
Localization and dimension free estimates for maximal functions
Alberto Criado, Fernando Soria
In the recent paper [J. Funct. Anal. {\bf 259} (2010)], Naor and Tao introduce a new class of measures with a so-called micro-doubling property and present, via martingale theory a…
A Widder's type Theorem for the heat equation with nonlocal diffusion
Begoña Barrios, Ireneo Peral, Fernando Soria +1
The main goal of this work is to prove that every non-negative {\it strong solution} to the problem $$ u_t+(-Δ)^{α/2}u=0 \ \quad\mbox{for } (x,t)\in\mathbb{R}^{n}\times(0,…
A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations
Pascal Bégout, Soria Fernando
In this paper, we establish a generalized H{ö}lder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabil…
Regularity of solutions of the fractional porous medium flow
Luis Caffarelli, Fernando Soria, Juan Luis Vazquez
We study a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. More precisely, $$ u_t=\nabla\cdot(u\nabla (-Δ)^{-s}u), \quad \…
On the growth of vector-valued Fourier series
Javier Parcet, Fernando Soria, Quanhua Xu
We prove the 'little Carleson theorem' on the growth of Fourier series for functions taking values in a UMD Banach space.
On the Boundedness in of the Maximal Square Function Associated with the Schroedinger Equation
Giacomo Gigante, Fernando Soria
A long standing conjecture for the linear Schroedinger equation states that 1/4 of derivative in , in the sense of Sobolev spaces, suffices in any dimension for the solution t…