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

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Author(s): Linfen Cao | Zhaohui Dai

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 01;
Start page: 153;
Date: 2013;
Original page

Keywords: Regularity Lifting | HLS Inequality | Contracting Operators | Shrinking Operators

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]).
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