Tomasz Jakubowski

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20102022

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math.AP2022

Estimates of gradient of $L$ -harmonic functions for nonlocal operators with order $α > 1$

Tomasz Grzywny, Tomasz Jakubowski, Grzegorz Żurek

We obtain Grönwall type estimates for the gradient of the harmonic functions for a Lévy operator with order strictly larger than 1 and minimal assumptions of its Lévy measure.

math.AP2022

Fractional Burgers equation with singular initial condition

Tomasz Jakubowski, Grzegorz Serafin

We consider the fractional Burgers equation $Δ^{α /2} u + b \cdot \nabla (u ∣ u ∣^{(α - 1) / β})$ on $R^{d}$ , $d \geq 2$ , with { $α \in (1, 2)$ and} $β > 1$ and prove the existence of a s…

math.AP2012

Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Piotr Graczyk, Tomasz Jakubowski, Tomasz Luks

Let $L = Δ^{α /2} + b \cdot \nabla$ with $α \in (1, 2)$ . We prove the Martin representation and the Relative Fatou Theorem for non-negative singular $L$ -harmonic functions on ${\mathcal C}^…

math.AP2010

Estimates of the Green function for the fractional Laplacian perturbed by gradient

Krzysztof Bogdan, Tomasz Jakubowski

The Green function of the fractional Laplacian of the differential order bigger than one and the Green function of its gradient perturbations are comparable for bounded smooth mult…

Estimates of gradient of L-harmonic functions for nonlocal operators with order α>1

Fractional Burgers equation with singular initial condition

Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Estimates of the Green function for the fractional Laplacian perturbed by gradient

Estimates of gradient of $L$ -harmonic functions for nonlocal operators with order $α > 1$