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

Original Paper

DOI: 10.1007/s00030-005-0031-6

Cite this article as:
Jakobsen, E.R. & Karlsen, K.H. Nonlinear differ. equ. appl. (2006) 13: 137. doi:10.1007/s00030-005-0031-6

Abstract.

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.

45K0549L2593E2060J75

Key words.

Integro-partial differential equationviscosity solutioncomparison principleuniquenessBellman equationIsaacs equation

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of MathematicsUniversity of BergenBergenNorway
  3. 3.Center of Mathematics for Applications, Department of MathematicsUniversity of OsloOsloNorway