# Mathematical Sciences Research Institute

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# Seminar

Harmonic Analysis Seminar: Regularity of the free boundary of almost minimizers for the Alt-Caffareli-Friedman functional February 27, 2017 (02:00 PM PST - 03:00 PM PST)
Parent Program: Harmonic Analysis MSRI: Simons Auditorium
Speaker(s) Guy DAVID (Université de Paris XI)
Description No Description
Video
We consider the same free boundary functional $J$ as Alt, Caffareli, and Friedman, but consider only almost minimizers $u$, and prove some regularity results for $u$ and the free boundary $\partial \{ u(x) > 0 \}$. The best results (local $C^1$
free boundary neat a flat point) concern the functional with only one phase. Recall that $J$ looks like this locally:
$$J(u) = \int |nabla u(x)|^2 + q_+(x) 1_{\{ u(x) > 0 \} } + q_-(x) 1_{\{ u(x) > 0 \} }$$ for some fixed bounded functions $q_\pm$ that are often assumed bounded from below.