Non-local gradient dependent operators

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• 作者：C. Bjorland ^{bjorland@math.utexas.edu} ; L. Caffarelli ^{caffarel@math.utexas.edu} ; A. Figalli ; ^{figalli@math.utexas.edu}
• 关键词：Quasilinear non-local operators ; Tug-of-war ; Existence ; Regularity
• 刊名：Advances in Mathematics
• 出版年：2012
• 期刊代码：62_00018708
• 类别：mt
• 出版时间：July-August, 2012
• 卷：230
• 期：4-6
• 页码：1859-1894
• 文件大小：342 K

摘要

In this paper we study a general class of 鈥渜uasilinear non-local equations鈥?depending on the gradient which arises from tug-of-war games. We establish a regularity theory for these equations (the kind of regularity depending on the assumptions on the kernel), and we construct different non-local approximations of the -Laplacian.