  In this paper we show that the map % $$\partial:CH^2(E_1 \times E_2,1)\otimes
\Q \longrightarrow PCH^1(\XX_v)$$ % is surjective, where $E_1$ and $E_2$ are
two non-isogenous semistable elliptic curves over a local field, $CH^2(E_1
\times E_2,1)$ is one of Bloch's higher Chow groups and $PCH^1(\XX_v)$ is a
certain subquotient of a Chow group of the special fibre $\XX_{v}$ of a
semi-stable model $\XX$ of $E_1 \times E_2$. On one hand, this can be viewed as
a non-Archimedean analogue of the Hodge-$\D$-conjecture of Beilinson - which is
known to be true in this case by the work of Chen and Lewis \cite{lech}, and on
the other, an analogue of the works of Spei{\ss} \cite{spie}, Mildenhall
\cite{mild} and Flach \cite{flac} in the case when the elliptic curves have
split multiplicative reduction.
