On the problem of unique continuation for the p-Laplace equation

We study if two different solutions of the $p$-Laplace equation $$\mathrm{\nabla }\cdot (\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{p-2}\mathrm{\nabla }u)=0,$$ where $1<p<\mathrm{\infty }$, can coincide in an open subset of their common domain of definition. We obtain some partial results on this interesting problem.