6 citations · 13 across the 17 of their papers we have counts for
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Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems
Boumediene Abdellaoui, Somia Atmani, Kheireddine Biroud +1
In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, o…
Fractional heat equation involving Hardy-Leray Potential
Boumediene Abdellaoui, Giovanni Siclari, Ana Primo
In this paper we analyse the existence and non-existence of non-negative solutions to a non-local parabolic equation with a Hardy-Leray type potential. More precisely, we consider…
Deterministic KPZ-type equations with nonlocal "gradient terms"
Boumediene Abdellaoui, Antonio J. Fernández, Tommaso Leonori +1
The main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local "gradient terms". More precisel…
Global fractional Calderón-Zygmund type regularity
Boumediene Abdellaoui, Antonio J. Fernández, Tommaso Leonori +1
We obtain a global fractional Calderón-Zygmund regularity theory for the fractional Poisson problem. More precisely, for , , a bounded domain with…
A note on quasilinear equations with fractional diffusion
Boumediene Abdellaoui, Pablo Ochoa, Ireneo Peral
In this paper, we study the existence of distributional solutions of the following non-local elliptic problem \begin{eqnarray*} \left\lbrace \begin{array}{l} (-Δ)^{s}u + |\nabla u|…
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…