Abstract
We prove comparison theorems and uniqueness of viscosity solutions for a class of nonlocal equations. This class of equations includes Bellman–Isaacs equations containing operators of Lévy type with measures depending on x and control parameters, as well as elliptic nonlocal equations that are not strictly monotone in the u variable. The proofs use the knowledge about regularity of viscosity solutions of such equations.
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Mou, C., Świe̜ch, A. Uniqueness of viscosity solutions for a class of integro-differential equations. Nonlinear Differ. Equ. Appl. 22, 1851–1882 (2015). https://doi.org/10.1007/s00030-015-0347-9
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DOI: https://doi.org/10.1007/s00030-015-0347-9