Ahmed Dughayshim

activity

20242026

collaborators

5 papers

math.AP2026

Global existence of the $s$ -Schrödinger maps in $n \geq 5$

Ahmed Dughayshim, Armin Schikorra

We study the $s$ -Schrödinger map equation \[ \begin{cases} \partial_t u = -u \wedge (-Δ)^s u \quad \text{on } \mathbb{R}^n \times \mathbb{R}\\ u: \mathbb{R}^n \times \mathbb{R} \to…

math.AP2026

The Trudinger inequality is true for $M^{1, s}$ spaces

Ryan Alvarado, Ahmed Dughayshim, Piotr Hajłasz

We prove the Trudinger inequality with exponent $\frac{s}{s - 1}$ for $M^{1, s}$ Sobolev spaces on metric measure spaces under the sole measure growth assumption $μ (B (x, r)) \geq b r^{s}$ .…

math.AP2025

On well-posedness of the s-Schrödinger maps in the subcritical regime

Ahmed Dughayshim

We study well-posedness of the $s$ -Schrödinger map equation in dimension $n \geq 3$ in the subcritical regime, more precisely we establish a local well-posedness result when the in…

math.AP2025

Local well-posedness for cubic fractional Schrödinger equations with derivatives on the right-hand side

Ahmed Dughayshim, Silvino Reyes Farina, Armin Schikorra

For $s \in (\frac{1}{2}, 1]$ we investigate well-posedness of the equation \[ \left ( i \partial_t + (-Δ)^{s} \right ) u = \left (|D|^{1-2s} |u|^2 \right)\ |D|^{2s-1} u \] under sma…

math.AP2024

Asymptotic Behaviour of fractional seminorms

Ahmed Dughayshim

We obtain asymptotically sharp identification of fractional Sobolev spaces $W_{p, q}^{s}$ , extension spaces $E_{p, q}^{s}$ , and Triebel-Lizorkin spaces $F ˙_{p, q}^{s}$ . In particu…

Global existence of the s-Schrödinger maps in n≥5

The Trudinger inequality is true for M1,s spaces

On well-posedness of the s-Schrödinger maps in the subcritical regime

Local well-posedness for cubic fractional Schrödinger equations with derivatives on the right-hand side

Asymptotic Behaviour of fractional seminorms

Global existence of the $s$ -Schrödinger maps in $n \geq 5$

The Trudinger inequality is true for $M^{1, s}$ spaces