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
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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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