Regularity of Solutions to an Integral Equation on a Half-Space R₊ⁿ

Linfen Cao, Zhaohui Dai

College of Mathematics and Information Science, Henan Normal University, Xinxiang, China.
Department of Computer Science, Henan Normal University, Xinxiang, China.

DOI: 10.4236/apm.2013.31A021                

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]).

Keywords

Regularity Lifting; HLS Inequality; Contracting Operators; Shrinking Operators

Conflicts of Interest

The authors declare no conflicts of interest.

References

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