I am interested in analysis of PDEs in free boundary problems. Please recommend some sources for me to learn about this.
I would prefer Sobolev space setting as opposed to Holder spaces.
2026-04-24 05:16:53.1777007813
Where to start to learn about free boundary problems?
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I would recommend (without any reservations)
A Geometric Approach to Free Boundary Problems, by Luis Caffarelli & Sandro Salsa,
as both the authors are currently among the leaders in the area.
I would also recommend a good and pleasant reading by Avner Friedman:
http://www.ams.org/notices/200008/fea-friedman.pdf
It is to be noted that A. Friedman's book on the same topic (now in Dover edition) is where I learned (I am not an expert though). Nevertheless, it is not a reader friendly text.