Which kind of drugs get absorbed through epidermis?
According to a review (Prausnitz2004), marketed drugs with a dermal route of administration tend to fulfil the following criteria :


Small molecular size (&lt; 500 Da)
High lipophilicity
Small required dose (up to ~milligram)


This is a consequence of the structure of the skin (with a lipophilic stratum corneum, and low diffusion speed) and practical concerns (everything else equal, a higher dose would need more surface area).

Beyond "pure" diffusion, there has been much work on improving drug delivery through other means : chemical enhancers (ethanol or DMSO being classical member of this class), medical devices (microneedle patch, ultrasonic device), and other more exotic methods mentionned in the paper.

These criteria are also mentionned in (GoodmanGillman2006, chapter 26), with emphasis on concentration gradient being the driving force behind diffusion across the skin. This chapter also contain a list of commonly used transdermal/dermatological drug, and their use.