Remarks on the Fractional Laplacian with Dirichlet Boundary Conditions and Applications. (27th May 2016) - Constantin, Peter; Ignatova, Mihaela
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.