Context-free Grammar Exercise
I think you can solve this using this construct:

$$S \rightarrow ASA|BSB|ATA|BTB $$
$$T \rightarrow CAZC|CBZC$$
$$Z \rightarrow AZ|BZ|\epsilon$$
$$A \rightarrow a , B \rightarrow b, C \rightarrow c$$

First rule provides the $w$ and $w^R$ in the language, second rule makes sure $v \ge 1$ and has 1 c in both sides and third is just constructing the $v$ further. My assumption was your arrow on top of last $w$ was just meant it is reversed.