### On fractional Sobolev, Isoperimetric and Poincaré inequalities - *Unusual time!*

Analysis and Geometry Seminar

13th June 2019, 1:00 pm – 2:00 pm

Howard House, 4th Floor Seminar Room

My aim is to give a comprehensive overview on fractional Sobolev, Isoperimetric and Poincaré Inequalities. I will explain some analogies and differences with the corresponding local inequalities, symmetrization techniques, best constant problems, and other current challenges. In the end I shall mention two recent results: one on regional fractional Poincaré inequality on unbounded domains (work in collaboration with I. Chowdhury.,S. Firoz and P. Roy), and another on the fractional Michael-Simon Sobolev inequality (work in collaboration with X. Cabré and M. Cozzi).

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