IJPAM: Volume 55, No. 2 (2009)

A NOTE ON $A_p$ ESTIMATES FOR SOLUTIONS OF
A SEMI-LINEAR ELLIPTIC EQUATION ASSOCIATED
WITH SUPERCONDUCTIVITY

Junichi Aramaki
Department of Mathematical Sciences
Faculty of Science and Engineering
Tokyo Denki University
Hatoyama-Machi, Hiki-Gun, Saitama-Ken, 350-0394, JAPAN
e-mail: aramaki@mail.dendai.ac.jp


Abstract.We study the property of a solution for a semi-linear elliptic equation in general dimensional Euclidean space $\rr ^n$. In our previous paper, we have proved the doubling property and the strong unique continuation theorem of the solution. In this note, we shall show the $A_p$ property for the solution under some assumptions.

Received: August 5, 2009

AMS Subject Classification: 82D55, 47F05, 35J60

Key Words and Phrases: $A_p$ estimate, semi-linear elliptic equation, Ginzburg-Landau system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2