The smoothness of the free boundary for a class of vector-valued problems
Martin Fuchs · Communications in Partial Differential Equations · 1989
We consider a minimizer u: Rn Ω→n of Dirichlet's integral under the additional side condition In(.) ⊂ M for a smooth domain M⊂RN. Imposing certain geometric conditions on M we show that the coincidence set {x∊Ω: u(x) ∊ ∂M) is of locally finite perimeter in Ω. Moreover, we formulate a condition implying the regularity of the free boundary near a given point.