Coupling Lévy measures and comparison principles for viscosity solutions

Guillen, Nestor; Mou, Chenchen; Świȩch, Andrzej

doi:10.1090/tran/7877

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
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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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