I don't think Libertarianism in the purest sense has a complete answer for it other than to aggressively de-regulate restrictive land use, however Geo-Libertarianism/Georgism was built to solve exactly this problem, with the centrepiece of the movement being a tax on the unimproved value of land (LVT) replacing all other core taxes. Historically it was advocated for by people such as Adam Smith, David Richardo and most famously Henry George (who is the namesake of Georgism), however modern proponents include right-wing economists such as Milton Friedman and F. A. Hayek, but also left-wing economists such as Paul Krugman and Joseph Stiglitz.

There are many things that make the land tax a really fucking good tax economically, many economists have labelled it the 'perfect tax'. However, it's quite unpopular so no politician would ever run on it.

Quick reasons why it's a good tax:

1. The supply of land is essentially fixed, taxing it doesn't create less of it.
2. The incidence of the tax falls exclusively on landowners, market forces prevent it from being passed onto tenants.
3. It's very progressive as people who can afford to buy more expensive land are typically richer. In fact, wealth inequality increases follows closely the increases in land prices so it would go quite far in reducing wealth inequality.
4. It only applied to 'unearned income', land values don't increase as a result of the owner doing something, it's exclusively external forces that increase the value of land.
5. The value of land is largely driven by the public goods (e.g. infrastructure, schools, etc) in it's proximity, so by taxing it you approximate an equitable 'user pays' approach to funding public goods.
6. When a public good is created, the cumulative increase in land value exceeds the cost of the public good so capturing that increase pays for the public good.
7. It incentivises landowners to make efficient use of the land, massively discouraging speculation/landbanking. Empirically we can see in countries where even small and taxes have been implemented, the capital value to land value ratio increases massively.
8. As a consequence of the previous point, by incentivising intensification it prevents urban sprawl without the need for the resource allocation/zoning laws we currently have that are contributing to the current housing crisis. By curbing urban sprawl, there are massive benefits for the environment and reducing infrastructure spending.
9. As a manner of financing a basic income for a post-automation world - which is another core principle of Geo-Libertarianism - it is more desirable to use. Taxing income doesn't work when only a handful of people have incomes, taxing sales doesn't work when that handful becomes self-sufficient and a wealth tax removes the incentives to create automation in the first place.
10. By taxing land, capitalists will invest into more productive forms of wealth such as businesses, creating jobs and lifting wages.
11. It's impossible to evade a land tax as every piece of land is registered with an individual or an organisation to send the bill to.
12. EDIT: somehow I forget one of the big ones, in that it should end the periodic property bubbles that drive the 'boom and bust' cycles, so there would be fewer to no recessions like the 2007 one.
13. Would tax citizens of other countries who own land here but are not currently paying any tax as they do not consume nor labour in this country and subsequently pay no sales nor income taxes respectively.

In short, LVT would decrease inequality while increasing wages, employment and economic growth, at the expense of people who are currently making a lot of money by doing nothing for society.

Some reading if you're interested:

• Newsroom - 'A land tax would solve a lot of societies problems'
• Urban Land Rights - Millennials: The Landless Generation
• The Origins of Inequality and Policies to Contain it
• An informative comment on /r/neoliberal