In this article under assumption of "small" density for negativity set, we prove local Lipschitz regularity for the one phase minimization problem with free boundary for the functional
where are positive constants so that , is the characteristic function of set , is (smooth) domain and minimum is taken over a suitable subspace of .
Cite this article
Aram L. Karakhanyan, On the Lipschitz regularity of solutions of a minimum problem with free boundary. Interfaces Free Bound. 10 (2008), no. 1, pp. 79–86DOI 10.4171/IFB/180