Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 07, pp. 1-12.

Title: Unique continuation for solutions of $p(x)$-Laplacian equations

Authors: Johnny Cuadro (Univ. Autonoma Metropolitana, Mexico)
         Gabriel Lopez (Univ. Autonoma Metropolitana, Mexico)

Abstract: 
 We study the unique continuation  property for solutions
 to the quasilinear elliptic equation
 $$
 \hbox{div}(|\nabla u|^{p(x)-2}\nabla  u)
 +V(x)|u|^{p(x)-2}u=0\quad \hbox{in }\Omega,
 $$
 where $\Omega$  is a smooth bounded domain in $\mathbb{R}^N$ and
 $1<p(x)<N $ for $x$ in $\Omega$.

An addendum was attached on October 14, 2012. Ito corrects some misprints.
 
Submitted September 8, 2011. Published January 12, 2012.
Math Subject Classifications: 35D05, 35J60, 58E05.
Key Words: p(x)-Laplace operator; unique continuation.