Amal Attouchi

activity

20122019

most citedGradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations

11 citations · 15 across the 10 of their papers we have counts for

collaborators

12 papers

math.AP2019

Gradient regularity for a singular parabolic equation in non-divergence form

Amal Attouchi, Eero Ruosteenoja

In this paper we consider viscosity solutions of a class of non-homogeneous singular parabolic equations $\partial_{t} u - ∣ D u ∣^{γ} Δ_{p}^{N} u = f,$ where $- 1 < γ < 0$ , $1 < p < \infty$ , and $f$ is…

math.AP2019★ 11 cited

Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations

Amal Attouchi, Philippe Souplet

Consider the diffusive Hamilton-Jacobi equation $u_{t} - Δ u = ∣\nabla u ∣^{p} + h (x) in Ω \times (0, T)$ with Dirichlet conditions, which arises in stochastic control problems as w…

math.AP2019

Gradient and Lipschitz estimates for tug-of-war type games

Amal Attouchi, Hannes Luiro, Mikko Parviainen

We define a random step size tug-of-war game, and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are unifo…

math.AP2018

Local regularity for quasi-linear parabolic equations in non-divergence form

Amal Attouchi

We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the $p$ -Laplacian type and in non-divergence form. We provide local Hölder and Lip…

math.AP2017

Remarks on regularity for $p$ -Laplacian type equations in non-divergence form

Amal Attouchi, Eero Ruosteenoja

We study a singular or degenerate equation in non-divergence form modeled by the $p$ -Laplacian, $- ∣ D u ∣^{γ} (Δ u + (p - 2) Δ_{\infty}^{N} u) = f in Ω.$ We investiga…

math.AP2016★ 1 cited

Hölder regularity for the gradient of the inhomogeneous parabolic normalized $p$ -Laplacian

Amal Attouchi, Mikko Parviainen

In this paper we study an evolution equation involving the normalized $p$ -Laplacian and a bounded continuous source term. The normalized $p$ -Laplacian is in non divergence form and…

math.AP2016

$C^{1, α}$ regularity for the normalized $p$ -Poisson problem

Amal Attouchi, Mikko Parviainen, Eero Ruosteenoja

We consider the normalized $p$ -Poisson problem $- Δ_{p}^{N} u = f in Ω.$ The normalized $p$ -Laplacian $Δ_{p}^{N} u := ∣ D u ∣^{2 - p} Δ_{p} u$ is in non-divergence form and arise…

math.AP2014★ 1 cited

Gradient estimate and a Liouville theorem for a $p$ -Laplacian evolution equation with a gradient nonlinearity

Amal Attouchi

In this paper, we establish a local gradient estimate for a $p$ -Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville…

math.AP2014

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$ -Laplacian diffusion

Amal Attouchi, Philippe Souplet

We study the initial-boundary value problem for the Hamilton-Jacobi equation with nonlinear diffusion $u_{t} = Δ_{p} u + ∣\nabla u ∣^{q}$ in a two-dimensional domain for $q > p > 2$ . It is known…

math.AP2013

Global Continuation beyond Singularities on the Boundary for a Degenerate Diffusive Hamilton-Jacobi Equation

Amal Attouchi, Guy Barles

In this article, we are interested in the Dirichlet problem for parabolic viscous Hamilton-Jacobi Equations. It is well-known that the gradient of the solution may blow up in finit…

math.AP2012★ 2 cited

Boundedness of global solutions of a p-Laplacian evolution equation with a nonlinear gradient term

Amal Attouchi

We investigate the boundedness and large time behavior of solutions of the Cauchy-Dirichlet problem for the one-dimensional degenerate parabolic equation with gradient nonlinearity…

math.AP2012

Well-posedness and gradient blow-up estimate near the boundary for a Hamilton-Jacobi equation with degenerate diffusion

Amal Attouchi

This paper is concerned with weak solutions of the degenerate viscous Hamilton-Jacobi equation $\partial_{t} u - Δ_{p} u = ∣\nabla u ∣^{q},$ with Dirichlet boundary conditions in a bounded…

Gradient regularity for a singular parabolic equation in non-divergence form

Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations

Gradient and Lipschitz estimates for tug-of-war type games

Local regularity for quasi-linear parabolic equations in non-divergence form

Remarks on regularity for p-Laplacian type equations in non-divergence form

Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian

C1,α regularity for the normalized p-Poisson problem

Gradient estimate and a Liouville theorem for a p-Laplacian evolution equation with a gradient nonlinearity

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with p-Laplacian diffusion

Global Continuation beyond Singularities on the Boundary for a Degenerate Diffusive Hamilton-Jacobi Equation

Boundedness of global solutions of a p-Laplacian evolution equation with a nonlinear gradient term

Well-posedness and gradient blow-up estimate near the boundary for a Hamilton-Jacobi equation with degenerate diffusion

Remarks on regularity for $p$ -Laplacian type equations in non-divergence form

Hölder regularity for the gradient of the inhomogeneous parabolic normalized $p$ -Laplacian

$C^{1, α}$ regularity for the normalized $p$ -Poisson problem

Gradient estimate and a Liouville theorem for a $p$ -Laplacian evolution equation with a gradient nonlinearity

Single point gradient blow-up on the boundary for a Hamilton-Jacobi equation with $p$ -Laplacian diffusion