Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 263, pp. 1-5.
Title: A note on p(x)-harmonic maps
Authors: Bei Wang (Jiangsu Institute of Education, Nanjing, China)
Yuze Cai (Shazhou Professional Institute of Technology, Jiangsu, China)
Abstract:
This article is concerned with L^{p(x)} estimates of the gradient of
p(x)-harmonic maps. It is known that p(x)-harmonic maps are the weak
solutions of a system with natural growth conditions, but
it is difficult to use the classical elliptic techniques to find
gradient estimates. In this article, we use the monotone inequality
to show that the minimum p(x)-energy can be expressed by the
L^{p(x)} norm of a gradient of a function Phi, which is a weak
solution of a single equation.
Submitted April 10, 2013. Published November 29, 2013.
Math Subject Classifications: 35J56, 35J70, 49J20, 58G18.
Key Words: Gradient estimate; p(x)-harmonic map; drill holes;
minimum p(x)-energy