Regularity for almost minimizers with free boundary

Tatiana Toro (November 14, 2011)

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Abstract

We study the regularity of almost minimizers for the types of functionals analyzed by Alt, Caffarelli and Freidman. Although almost minimizers do not satisfy an equation using appropriate comparison functions we prove several regularity results. For example in the one phase situation we show that almost minimizers are Lipschitz. Our approach reminiscent of the one used in geometric measure theory to study the regularity of almost minimizers for area. This project is joint work with Guy David.