Characterization of balls in terms of Bessel-potential integral equation

Abstract

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 method developed by Chen, Li and Ou (2006) in [7] to establish our main results. Show more