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Regularity of Solutions to an Integral Equation on a Half-Space <i>R<sub>+</sub><sup style=" margin-left:-5px; margin-bottom:-2px;">n</sup></i>
College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
Department of Computer Science, Henan Normal University, Xinxiang, China
- 1 College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
- 2 Department of Computer Science, Henan Normal University, Xinxiang, China
Advances in Pure Mathematics·Volume 03 (2013)·Pages 153–158·Published 30 January 2013·DOI10.4236/apm.2013.31A021
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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]).
KeywordsRegularity LiftingHLS InequalityContracting OperatorsShrinking Operators
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