IJPAM: Volume 49, No. 1 (2008)

APPROXIMATION OF HARMONIC FUNCTIONS IN
SOBOLEV SPACES

Yingchun Jiang$^1$, Hong Wang$^2$
$^1$School of Mathematics and Computational Science
Guilin University of Electronic Technology
Guilin, 541004, P.R. CHINA
e-mail: guilinjiang@126.com
$^2$China Civil Affairs College
Beijing, 101601, P.R. CHINA
e-mail: wanghong2000@emails.bjut.edu.cn


Abstract.This paper is concerned with the regularity of harmonic functions which determines the efficiency of approximation in Sobolev space $W^{t, p}(\Omega)$. The result shows that the nonlinear approximation is always superior to linear approximation for harmonic functions on bounded Lipschitz domain.

Received: September 23, 2008

AMS Subject Classification: 42C15, 94A11

Key Words and Phrases: nonlinear approximation, wavelets, harmonic functions, Sobolev spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 1