We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear driftdiffusion equations with nonlocal dissipation and global existence of weak solutions of critical surface quasi-geostrophic equations.
|Original language||English (US)|
|Number of pages||21|
|Journal||International Mathematics Research Notices|
|State||Published - Mar 1 2017|
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