Fractional Laplacian with singular drift

Tomasz Jakubowski. "Fractional Laplacian with singular drift." Studia Mathematica 207.3 (2011): 257-273. <http://eudml.org/doc/285519>.

@article{TomaszJakubowski2011,
abstract = {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.},
author = {Tomasz Jakubowski},
journal = {Studia Mathematica},
keywords = {fractional Laplacian; gradient perturbation},
language = {eng},
number = {3},
pages = {257-273},
title = {Fractional Laplacian with singular drift},
url = {http://eudml.org/doc/285519},
volume = {207},
year = {2011},
}

TY - JOUR
AU - Tomasz Jakubowski
TI - Fractional Laplacian with singular drift
JO - Studia Mathematica
PY - 2011
VL - 207
IS - 3
SP - 257
EP - 273
AB - 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.
LA - eng
KW - fractional Laplacian; gradient perturbation
UR - http://eudml.org/doc/285519
ER -