2007/02/28 by Guy Barles, Cyril Imbert
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Fractional Differential Equations Solutions #Nonlinear Partial Differential Equations #math.AP #msc:35B05 #msc:35D99 #msc:35J60 #msc:47G20
paper · pdf · doi:10.1016/j.anihpc.2007.02.007
published as Annales de l'Institut Henri Poincaré Analyse non linéaire 25, 3 (2008) 567-585
openalex publication_date 2007/07/31 · arxiv created 2008/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen–Ishii's lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The proof of this result, which is of course a key ingredient to prove comparison principles, relies on a new definition of viscosity solution for integro-differential equation (equivalent to the two classical ones) which combines the approach with test-functions and sub-superjets.