Electron. J. Diff. Equ., Vol. 2013 (2013), No. 263, pp. 1-5.

A note on p(x)-harmonic maps

Bei Wang, Yuze Cai

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
  Yuze Cai
Department of Basic Science
Shazhou Professional Institute of Technology
Zhangjiagang, Jiangsu 215600, China
email: caibcd@163.com

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