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Characterization of balls in terms of Bessel-potential integral equation

Han, Xiaolong; Lu, Guozhen; Zhu, Jiuyi

Description

For a bounded C1 domain O ? RN , we consider the Bessel potential u(x) = O ga(x - y)dy for 2 a < N. We show that u = constant on ?O if and only if O is a ball. More general Bessel-potential integral equation u(x) = O ga(x - y)h u(y) dy is also studied. Similar characterization of balls holds under certain assumptions on u and h(u(y)). We will use an integral form of the celebrated Alexandroff (1962) [2], Serrin (1971) [28], and Gidas, Ni and Nirenberg (1979) [16], (1981) [17] moving plane...[Show more]

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
URI: http://hdl.handle.net/1885/98964
Source: Journal of Differential Equations
DOI: 10.1016/j.jde.2011.07.037

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