Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
This is joint work with Max Engelstein and Tatiana Toro.
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)=∫|nablau(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.