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A Holder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions

Authors
Kim, IldooKim, Kyeong-Hun
Issue Date
11월-2015
Publisher
SPRINGER
Keywords
Non-local elliptic equations; Integro-differential equations; Non-symmetric measurable kernels; Holder estimates; Subordinate Brownian motion
Citation
POTENTIAL ANALYSIS, v.43, no.4, pp.653 - 673
Indexed
SCIE
SCOPUS
Journal Title
POTENTIAL ANALYSIS
Volume
43
Number
4
Start Page
653
End Page
673
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/92096
DOI
10.1007/s11118-015-9490-5
ISSN
0926-2601
Abstract
In this article we present the existence, uniqueness, and Holder regularity of solutions for the non-local elliptic equations of the type Lu-lambda u = f in R-d, where Lu(x) = integral(Rd) (u(x + y) - u(x) - y.del u(x)chi(y)) a(y) J (y) dy. Here chi(y) is a suitable indicator function, J(y) dy is a rotationally invariant Levy measure on R-d (i. e. integral(Rd) (1 boolean AND vertical bar y vertical bar(2) )J(y) dy < infinity), and a(y) is an only measurable function with positive lower and upper bounds.
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