Regularity of solutions to an integral equation associated with Bessel potential

Xiaolong Han; Guozhen Lu

doi:10.3934/cpaa.2011.10.1111

Article Contents

2011, Volume 10, Issue 4: 1111-1119. Doi: 10.3934/cpaa.2011.10.1111

This issue Previous Article The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis Next Article Remarks on some dispersive estimates

Regularity of solutions to an integral equation associated with Bessel potential

Xiaolong Han^1, and
Guozhen Lu^1,

1.
Department of Mathematics, Wayne State University, Detroit, MI 48202

Received: July 2010

Revised: December 2010

Published: July 2011

Abstract / Introduction Related Papers Cited by

Abstract

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].

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Mathematics Subject Classification: Primary: 45E10; Secondary: 35J60.

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