平特五不中

Title: Almost minimizers with free boundary

Abstract: In recent work with G. David, and ongoing work with G. David and M. Engelstein, we study almost minimizer for functionals which yield a free boundary, as in the work of Alt-Caffarelli and Alt-Caffarelli-Friedman. The almost minimizing property can be understood as the defining characteristic of a minimizer in a problem which explicitly takes noise into account. In this talk we will discuss regularity results for these almost minimizers and as well as the structure of the corresponding free boundary. A key ingredient in the study of the 2-phase problem is the existence of almost monotone quantities.