Fractional Laplacian with singular drift

• Autorzy: Tomasz Jakubowski
• Języki publikacji: EN

Abstrakty

EN

For α ∈ (1,2) we consider the equation $∂_t u = Δ^{α/2}u + b·∇u$, where b is a time-independent, divergence-free singular vector field of the Morrey class $M₁^{1-α}$. We show that if the Morrey norm $||b||_{M₁^{1-α}}$ is sufficiently small, then the fundamental solution is globally in time comparable with the density of the isotropic stable process.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 207
• Numer: 3
• Strony: 257-273

Daty

wydano

2011

Twórcy

autor

Tomasz Jakubowski

• Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm207-3-3