Abstract
AbstractIn this section, we will prove that the local minimizers of
$$\mathcal F_\Lambda $$
ℱ
Λ
are Lipschitz continuous. Our main result is the following.
Publisher
Springer International Publishing
Reference11 articles.
1. H.W. Alt, L.A. Caffarelli, Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math. 325, 105–144 (1981)
2. H.W. Alt, L.A. Caffarelli, A. Friedman, Variational problems with two phases and their free boundaries. Trans. Amer. Math. Soc. 282(2), 431–461 (1984)
3. T. Briançon, M. Hayouni, M. Pierre, Lipschitz continuity of state functions in some optimal shaping. Calc. Var. PDE 23(1), 13–32 (2005)
4. D. Bucur, D. Mazzoleni, A. Pratelli, B. Velichkov, Lipschitz regularity of the eigenfunctions on optimal domains. Arch. Ration. Mech. Anal. 216(1), 117–151 (2015)
5. D. Danielli, A. Petrosyan, A minimum problem with free boundary for a degenerate quasilinear operator. Calc. Var. PDE 23(1), 97–124 (2005)