Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications

Peter Constantin; Mihaela Ignatova

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arXiv · 1511.00147

Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications

Peter Constantin·Mihaela Ignatova

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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.

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Peter Constantin, Mihaela Ignatova. 2015-10-31. Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications. https://arxiv.org/abs/1511.00147

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