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 Abstract: We consider the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove global a priori interior $C^{\alpha}$ and Lipschitz bounds for large data. Publication Date: 2016 Electronic Publication Date: 30-Nov-2016 Citation: Constantin, Peter, and Mihaela Ignatova. "Critical SQG in bounded domains." Annals of PDE 2.2 (2016): 8. DOI: 10.1007/s40818-016-0017-1 Pages: 8:1-42 Type of Material: Journal Article Journal/Proceeding Title: Annals of PDE Version: Author's manuscript