TITLE:
Regularity of Solutions to an Integral Equation on a Half-Space R+n
AUTHORS:
Linfen Cao, Zhaohui Dai
KEYWORDS:
Regularity Lifting; HLS Inequality; Contracting Operators; Shrinking Operators
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.1A,
January
30,
2013
ABSTRACT:
In this paper, we discuss the integral equation on a half space R+n
where is the reflection of the point x about the . We study the regularity for the positive solutions of (0.1). A regularity lifting method by contracting operators is used in proving the boundedness of solutions, and the Lipschitz continuity is derived by combinations of contracting and shrinking operators introduced by Ma-Chen-Li ([1]).