The question as to whether it is possible to buy/own land in Antarctic is a yes and no question. It is a no based on the present circumstances and a yes on the basis of current events taking place on the fifth largest continent on earth. A short history is appropriate to make the yes and no answers clear.
From the onset, Antarctic does not have any known native population. It is widely believed that it was initially part of a large mass of land known as Gondwana covering the South Pole. The present Antarctic eventually split from both Australasia and South America long before evolution of mankind, which only occurred about 5 million years ago. Antarctic has remained de-linked from the rest of the world for over the last 30 million years.
Antarctic lies in the Antarctic region on the southernmost end of the earth. Its geographical region covers South Pole and is surrounded by the Southern Ocean. A big chunk of its mass (98%) is covered by ice measuring about 1.2 km in thickness. It is the coldest, windiest and driest of all continents. This makes it the most extreme geographical region of the earth.
Technological advancements realized over the years have made it possible for humans to set foot in Antarctic. It is currently home to about 1,500 and 5,000 people during winter and summer respectively. However, these people do not call Antarctic home. They are mostly researchers and tourists. Indeed, there are over 60 scientific research bases on the continent of which about 37 are always occupied at any given time.
Several countries including UK, New Zealand, France, Norway, Australia, Chile and Argentina have laid claims to specific regions of Antarctic. Indeed, the research stations in Antarctic are set up and manned by scientist from these countries. However, territorial claims have remained suspended since 1959. Even so, a negotiated Antarctic Treaty System was put in place in 1983 for regulation of mining activities on the continent. Signed by 12 countries including US, Argentina, Australia, Chile and the then Soviet Union (now Russia), the treaty preserves Antarctic as a scientific research location.
Is it possible to buy/own land in Antarctic? No because there is no authority to regulate such a transaction. It is also no because the Antarctic Treaty System in place forbids any form of settlement other than for the purpose of research. It is also a yes because there are settlements in Antarctic even though they are for scientific purpose. The fact that there are school systems, medical facilities and an Orthodox church in Antarctic gives the impression that it will be possible in the future to buy/own land in Antarctic. There is no doubt that the existing suspension on territorial claims that has been in place since 1959 will eventually be uplifted to pave way for general settlement in Antarctic, at least in the different territories claimed so far. It is just a matter of time.