Geodesic
A note on \(p(x)\)-harmonic maps
Electronic journal of differential equations, Tome 2013 (2013)
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.
Classification : 35J56, 35J70, 49J20, 58G18
Keywords: gradient estimate, $p(x)$-harmonic map, drill holes, minimum $p(x)$-energy 
@article{EJDE_2013__2013__a52,
     author = {Wang,  Bei and Cai,  Yuze},
     title = {A note on \(p(x)\)-harmonic maps},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.35235},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a52/}
}
TY  - JOUR
AU  - Wang,  Bei
AU  - Cai,  Yuze
TI  - A note on \(p(x)\)-harmonic maps
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a52/
LA  - en
ID  - EJDE_2013__2013__a52
ER  - 
%0 Journal Article
%A Wang,  Bei
%A Cai,  Yuze
%T A note on \(p(x)\)-harmonic maps
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a52/
%G en
%F EJDE_2013__2013__a52
Wang,  Bei; Cai,  Yuze. A note on \(p(x)\)-harmonic maps. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a52/