`a`

Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations

Pages: 164 - 172, Issue Special, August 2005

 Abstract        Full Text (216.5K)              

Wenxiong Chen - Department of Mathematics, Yeshiva University, New York, NY 10033, United States (email)
Chao Jin - Department of Applied Mathematics, University of Colorado at Boulder, United States (email)
Congming Li - Department of Applied Mathematics, University of Colorado at Boulder, United States (email)
Jisun Lim - Department of Applied Mathematics, University of Colorado at Boulder, Campus Box 526, Boulder, CO 80309-0526, United States (email)

Abstract: In this paper, we consider systems of integral equations related to the weighted Hardy-Littlewood-Sobolev inequality. We present the symmetry, monotonity, and regularity of the solutions. In particular, we obtain the optimal integrability of the solutions to a class of such systems. We also present a simple method for the study of regularity, which has been extensively used in various forms. The version we present here contains some new developments. It is much more general and very easy to use. We believe the method will be helpful to both experts and non-experts in the field.

Keywords:  Weighted Hardy-Littlewood-Sobolev inequalities, integral equations and systems, radial symmetry, monotonicity, moving planes in integral forms.
Mathematics Subject Classification:  35J99, 45E10, 45G05.

Received: September 2004;      Revised: February 2005;      Published: September 2005.