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

Ildoo Kim; Kyeong Hun Kim

doi:10.1016/j.jmaa.2015.09.075

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

Ildoo Kim, Kyeong Hun Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 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 L_p-spaces and present some L_p-estimates of the solutions.

Original language	English
Pages (from-to)	1302-1335
Number of pages	34
Journal	Journal of Mathematical Analysis and Applications
Volume	434
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.09.075
Publication status	Published - 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

Access to Document

10.1016/j.jmaa.2015.09.075

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)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.",

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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)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.

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)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.

KW - Integro-differential equations

KW - Lévy processes

KW - Non-local elliptic equations

KW - Non-symmetric measurable kernels

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