# American Institute of Mathematical Sciences

July  2011, 10(4): 1111-1119. doi: 10.3934/cpaa.2011.10.1111

## Regularity of solutions to an integral equation associated with Bessel potential

 1 Department of Mathematics, Wayne State University, Detroit, MI 48202, United States

Received  July 2010 Revised  December 2010 Published  April 2011

In this paper, we study the regularity of the positive solutions to an integral equation associated with the Bessel potential. The kernel estimates for the Bessel potential plays an essential role in deriving such regularity results. First, we apply the regularity lifting by contracting operators to get the $L^\infty$ estimate. Then, we use the regularity lifting by combinations of contracting and shrinking operators, which was recently developed in [4] and [5], to prove the Lipschitz continuity estimate. Our regularity results here have been recently extended to positive solutions to an integral system associated with Bessel potential [9].
Citation: Xiaolong Han, Guozhen Lu. Regularity of solutions to an integral equation associated with Bessel potential. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1111-1119. doi: 10.3934/cpaa.2011.10.1111
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