Work

Second-order elliptic integro-differential equations: viscosity solutions' theory revisited

Year: 2007

Type: article

Abstract: 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.

Source: Annales de l Institut Henri Poincaré C Analyse Non Linéaire

DOI: 10.1016/j.anihpc.2007.02.007

Authors: Guy Barles, Cyril Imbert

Institutions: Université de Tours, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques et Physique Théorique, Institut Montpelliérain Alexander Grothendieck, Université Montpellier 2

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W2035637414

FWCI: 15.32

Cites: 19

Cited by: 342

Related to: 8