Electron. J. Diff. Equ., Vol. 2012 (2012), No. 07, pp. 1-12.

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

Johnny Cuadro, Gabriel Lopez

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. It corrects some misprints. See the last page of this article.

Submitted September 8, 2011. Published January 12, 2012.
Math Subject Classifications: 35D05, 35J60, 58E05.
Key Words: p(x)-Laplace operator; unique continuation.

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Johnny Cuadro M.
Universidad Autónoma Metropolitana
Mexico D. F., Mexico
email: jcuadrom@yahoo.com
Gabriel López G.
Universidad Autónoma Metropolitana
Mexico D. F., Mexico
email: jcuadrom@yahoo.com

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