Fractional Laplacian with singular drift

Tomasz Jakubowski

Studia Mathematica, Tome 204 (2011), p. 257-273 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Publié le : 2011-01-01

Zbl 1242.60081

EUDML-ID : urn:eudml:doc:285519

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     author = {Tomasz Jakubowski},
     title = {Fractional Laplacian with singular drift},
     journal = {Studia Mathematica},
     volume = {204},
     year = {2011},
     pages = {257-273},
     zbl = {1242.60081},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-3-3}
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Tomasz Jakubowski. Fractional Laplacian with singular drift. Studia Mathematica, Tome 204 (2011) pp. 257-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-3-3/