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Could someone recommend some notes/papers that deal with existence/regularity of free boundary problems arising from parabolic equations (excluding Stefan type equations)?

I am thinking of eg. degenerate equations where solutions are compactly supported (given appropriate data) which gives rise to a free boundary.

I have seen such papers. But they are difficult to follow "the big idea" because there are lots of small lemmas and estimates and I cannot see how they relate to the big picture. Thus I am seeking something nice to read.

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“A geometric approach to free boundary problems ”by L.A. Caffarelli, and S. Salsa is an excellent textbook on parabolic free boundary problems. However, it may not be suitable for beginners, and for readers who are new to free boundary problems, “Regularity of the One-phase Free Boundaries” by Bozhidar Velichkov is an easy-to-read introductory textbook, although it is not about the parabolic problem. But I think there are probably very few textbooks on free boundaries that start with the parabolic case.

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