Department of Mathematics

Analysis and PDE

  •  Nestor Guillen, University of Massachusetts at Amherst
  •  Transportation methods for Lévy measures and applications
  •  04/24/2019
  •  4:10 PM - 5:00 PM
  •  C517 Wells Hall

The comparison principle for second order elliptic equations is one of the cornerstone of the theory of viscosity solutions. Works of Sayah and more recently by Jakobsen-Karlsen and Barles-Imbert have expanded it to many important subfamilies of nonlocal elliptic equations. In joint work with Chenchen Mou and Andrzej Święch we show how optimal transportation methods can be used to couple Lévy measures, which encode the integro-differential part of nonlocal operators, which allow us to obtain comparison principles for new families of nonlocal equations. Our method puts all previous subfamilies of nonlocal operators (Levy-Ito operators, operators of order less than 1) in a single framework, while also yielding results for new families.

 

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Department of Mathematics
Michigan State University
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