Coupling Lévy measures and comparison principles for viscosity solutions
Authors:
Nestor Guillen, Chenchen Mou and Andrzej Świȩch
Journal:
Trans. Amer. Math. Soc. 372 (2019), 7327-7370
MSC (2010):
Primary 35D40, 35J60, 35R09, 45K05, 47G20
DOI:
https://doi.org/10.1090/tran/7877
Published electronically:
August 28, 2019
MathSciNet review:
4024555
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove new comparison principles for viscosity solutions of nonlinear integro-differential equations. The operators to which the method applies include but are not limited to those of Lévy-Itô type. The main idea is to use an optimal transport map to couple two different Lévy measures and use the resulting coupling in a doubling of variables argument.
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Additional Information
Nestor Guillen
Affiliation:
Department of Mathematics and Statistics, UMass, Amherst, Massachusetts 01003
Email:
nguillen@math.umass.edu
Chenchen Mou
Affiliation:
Department of Mathematics, UCLA, Los Angeles, California 90095
Email:
muchenchen@math.ucla.edu
Andrzej Świȩch
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email:
swiech@math.gatech.edu
DOI:
https://doi.org/10.1090/tran/7877
Keywords:
Optimal transport,
L\'evy measures,
nonlocal equations,
viscosity solutions,
comparison principles,
uniqueness.
Received by editor(s):
July 12, 2018
Received by editor(s) in revised form:
April 1, 2019, and April 16, 2019
Published electronically:
August 28, 2019
Article copyright:
© Copyright 2019
American Mathematical Society