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Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels

Authors
Kim, Yong-CheolLee, Ki-Ahm
Issue Date
11월-2012
Publisher
SPRINGER
Citation
MANUSCRIPTA MATHEMATICA, v.139, no.3-4, pp.291 - 319
Indexed
SCIE
SCOPUS
Journal Title
MANUSCRIPTA MATHEMATICA
Volume
139
Number
3-4
Start Page
291
End Page
319
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/107099
DOI
10.1007/s00229-011-0516-z
ISSN
0025-2611
Abstract
In this paper, we consider fully nonlinear integro-differential equations with possibly nonsymmetric kernels. We are able to find different versions of Alexandroff-Backelman-Pucci estimate corresponding to the full class of uniformly elliptic nonlinear equations with 1 < sigma < 2 (subcritical case) and to their subclass with 0 < sigma a parts per thousand currency sign 1. We show that still includes a large number of nonlinear operators as well as linear operators. And we show a Harnack inequality, Holder regularity, and C (1,alpha) -regularity of the solutions by obtaining decay estimates of their level sets in each cases.
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Kim, Yong Cheol
사범대학 (수학교육과)
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