An Lp-theory for a class of non-local elliptic equations related to nonsymmetric measurable kernels

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    8 Citations (Scopus)

    Abstract

    We study the integro-differential operators L with kernels K(y)=a(y)J(y), where J(y) is rotationally invariant and J(y)dy is a Lévy measure on Rd (i.e. ∫Rd(1|y|2)J(y)dy<∞) and a(y) is an only measurable function with positive lower and upper bounds. Under few additional conditions on J(y), we prove the unique solvability of the equation Lu-λu=f in Lp-spaces and present some Lp-estimates of the solutions.

    Original languageEnglish
    Pages (from-to)1302-1335
    Number of pages34
    JournalJournal of Mathematical Analysis and Applications
    Volume434
    Issue number2
    DOIs
    Publication statusPublished - 2016 Feb 15

    Bibliographical note

    Publisher Copyright:
    © 2015 Elsevier Inc.

    Keywords

    • Integro-differential equations
    • Lévy processes
    • Non-local elliptic equations
    • Non-symmetric measurable kernels

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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