MPEPIL has useful introductory articles including 'Antarctica' by Silja Vöneky, Sange Addison-Agyei and 'Dispute Settlement under the Antarctic Treaty System by Donald R Rothwell
Antarctica in International Law by 
The Antarctic Environment and International Law by 
The Antarctic Environmental Protocol and Its Domestic Legal Implementation by Subject Searches to use in SOLO
Law -- Polar regions
Natural resources -- Law and legislation -- Polar regions
Law of the sea -- Polar regions
Polar law textbook by Arctic Studies:
You may need to consider the domestic law and legislation of the jurisdictions of Canada, Denmark, Finland, Iceland, Norway, Russian Federation, Sweden, and USA to understand the full extent of legal measures controlling the arctic region.