Is this what you are looking for??
You can get rid of the blank space using scales="free_y"
in the call to facet_wrap(...)
. This forces each facet to have it's own y-axis, but does not force the display of a separate x-axis on each facet. I also added a different color scale (take it out if you prefer the default).
library(ggplot2)
library(reshape2)
library(RColorBrewer)
ggplot(melt(v), aes(x=X1, y=X2)) +
facet_wrap(~ L1, ncol=1,scales="free_y") +
geom_tile(aes(fill=value)) + ggtitle("Title") +
scale_fill_gradientn(colours=rev(brewer.pal(9,"Spectral")))+
theme(plot.title = element_text(lineheight=2, face="bold"))