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A Holder Regularity Theory for a Class of Non-Local Elliptic Equations Related to Subordinate Brownian Motions
- Authors
- Kim, Ildoo; Kim, 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
- 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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