Uniqueness of viscosity solutions for a class of integro-differential equations

  • Chenchen Mou
  • Andrzej Świe̜chEmail author


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.

Mathematics Subject Classification

35R09 35D40 35J60 47G20 45K05 93E20 


Viscosity solution Integro-PDE Hamilton–Jacobi–Bellman–Isaacs equation Comparison theorem 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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