# Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications

## Author(s): Constantin, Peter; Ignatova, Mihaela

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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 drift-diffusion equations with nonlocal dissipation and global existence of weak solutions of critical surface quasi-geostrophic equations. Publication Date: Mar-2017 Electronic Publication Date: 28-May-2016 Citation: Constantin, P., & Ignatova, M. (2017). Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications. International Mathematics Research Notices, 2017(6), 1653-1673. DOI: 10.1093/imrn/rnw098 Pages: 1653–1673 Type of Material: Journal Article Journal/Proceeding Title: International Mathematics Research Notices Version: Author's manuscript