Remarks on the fractional laplacian with dirichlet boundary conditions and applications

Peter Constantin; Mihaela Ignatova

doi:10.1093/imrn/rnw098

Remarks on the fractional laplacian with dirichlet boundary conditions and applications

Peter Constantin
, Mihaela Ignatova

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

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)
Pages (from-to)	1653-1673
Number of pages	21
Journal	International Mathematics Research Notices
Volume	2017
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnw098
State	Published - Mar 1 2017

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnw098

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abstract = "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.",

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Remarks on the fractional laplacian with dirichlet boundary conditions and applications

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