Original Paper

Nonlinear Differential Equations and Applications NoDEA

, Volume 13, Issue 2, pp 137-165

First online:

A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations

  • Espen R. JakobsenAffiliated withDepartment of Mathematical Sciences, Norwegian University of Science and Technology Email author 
  • , Kenneth H. KarlsenAffiliated withDepartment of Mathematics, University of BergenCenter of Mathematics for Applications, Department of Mathematics, University of Oslo

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We formulate and prove a non-local “maximum principle for semicontinuous functions” in the setting of fully nonlinear and degenerate elliptic integro-partial differential equations with integro operators of second order. Similar results have been used implicitly by several researchers to obtain compare/uniqueness results for integro-partial differential equations, but proofs have so far been lacking.

2000 Mathematics Subject Classification.

45K05 49L25 93E20 60J75

Key words.

Integro-partial differential equation viscosity solution comparison principle uniqueness Bellman equation Isaacs equation