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

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2 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)dyp-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

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Integro-differential Operators
Lp Estimates
Nonlocal Equations
Elliptic Equations
kernel
Invariant
Class

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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title = "An Lp-theory for a class of non-local elliptic equations related to nonsymmetric measurable kernels",
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 L{\'e}vy measure on Rd (i.e. ∫Rd(1|y|2)J(y)dyp-spaces and present some Lp-estimates of the solutions.",
keywords = "Integro-differential equations, L{\'e}vy processes, Non-local elliptic equations, Non-symmetric measurable kernels",
author = "Ildoo Kim and Kim, {Kyeong Hun}",
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AU - Kim, Ildoo

AU - Kim, Kyeong Hun

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N2 - 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)dyp-spaces and present some Lp-estimates of the solutions.

AB - 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)dyp-spaces and present some Lp-estimates of the solutions.

KW - Integro-differential equations

KW - Lévy processes

KW - Non-local elliptic equations

KW - Non-symmetric measurable kernels

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JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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ER -