科研之友
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摘要
Let R(+)(n) be the n-dimensional upper half Euclidean space, and let alpha be any real number satisfying 0 < alpha < n. In this paper, we consider the integral equation (1) u(x) = integral(R+n) (1/vertical bar x-y vertical bar(n-alpha) - 1/vertical bar x*-y vertical bar(n-alpha)) u(tau) (y), u(x) > 0, for all x is an element of R(+)(n), where T = n + alpha/n - alpha, and x* = (x(1), ... , x(n-1), -x(n)) is the reflection of the point x about the hyperplane x(n) = 0. We use a new type of moving plane method in integral forms introduced by Chen, Li and Ou to establish the regularity and rotational symmetry of the solution of the above integral equation.
- 出版日期2010-8
- 单位河南师范大学
