IJPAM: Volume 18, No. 1 (2005)

HIGHER INTEGRABILITY FOR VERY WEAK
SOLUTIONS OF NONHOMOGENEOUS
$\cal A$ -HARMONIC EQUATION

Gao Hongya

, Zhang Hua

, Gao Chunxia

$^{1,2}$ College of Mathematics and Computer Science
Hebei University
Baoding, 071002, P.R. CHINA

e-mail: hongya-gao@sohu.com

e-mail: zhanghumaths@eyou.com

College of Electronic and Information Engineering
Hebei University
Baoding, 071002, P.R. CHINA
e-mail: chunxia-gao@163.com

Abstract.This paper gives a higher integrability result for very weak solutions of the nonhomogeneous $\cal A$ -harmonic equation

$\begin{displaymath} \mbox{div}{\cal A}(x,g(x)+\nabla u(x))=-f(x) \end{displaymath}$

by using the results of Riesz transforms and interpolation.

Received: November 12, 2004

AMS Subject Classification: 35J60

Key Words and Phrases: $\cal A$ -harmonic equation, very weak solution, Riesz transform, interpolation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 1

International Journal of Pure and Applied Mathematics - IJPAM