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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Kim, Ildoo¹  Kim, Kyeong-Hun¹ 

[1] Korea Univ, Dept Math, 1 Anam Dong, Seoul 136701, South Korea

关键词: Non-local elliptic equations;    Integro-differential equations;    Levy processes;    Non-symmetric measurable kernels;   

DOI  :  10.1016/j.jmaa.2015.09.075

来源: Elsevier

【 摘 要 】

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 Levy measure on R-d (i.e. integral(Rd) (1 Lambda vertical bar y vertical bar(2)) J(y)dy < infinity) 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 - lambda u = f in L-p-spaces and present some L-p-estimates of the solutions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free