Bei Wang, Yuze Cai
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
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Bei Wang School of mathematics and information technology Jiangsu Institute of Education Nanjing, Jiangsu 210013, China email: jsjywang@126.com |
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| Yuze Cai Department of Basic Science Shazhou Professional Institute of Technology Zhangjiagang, Jiangsu 215600, China email: caibcd@163.com |
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