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

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Espen R. Jakobsen

  2. Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, 5008, Bergen, Norway

    Kenneth H. Karlsen

  3. Center of Mathematics for Applications, Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    Kenneth H. Karlsen

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  1. Espen R. Jakobsen
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  2. Kenneth H. Karlsen
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Correspondence to Espen R. Jakobsen.

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Jakobsen, E.R., Karlsen, K.H. A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations. Nonlinear differ. equ. appl. 13, 137–165 (2006). https://doi.org/10.1007/s00030-005-0031-6

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  • DOI: https://doi.org/10.1007/s00030-005-0031-6

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