In this paper we complete the study of the regularity of the free boundary in two-phase problems for linear elliptic operators started in [M.C. Cerutti, F. Ferrari, S. Salsa, Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are C^{1,gamma} [Arch. Ration. Mech. Anal. 171 (2004) 329–348]. In particular we prove that Lipschitz and flat free boundaries (in a suitable sense) are smooth. As byproduct, we prove that Lipschitz free boundaries are smooth in the case of quasilinear operators of the form div(A(x,u)grad(u)) with Lipschitz coefficients.
F. Ferrari, S. Salsa (2007). Regularity of the free boundary in two-phase Problems for linear elliptic operators. ADVANCES IN MATHEMATICS, 214, 288-322 [10.1016/j.aim.2007.02.004].
Regularity of the free boundary in two-phase Problems for linear elliptic operators
FERRARI, FAUSTO;
2007
Abstract
In this paper we complete the study of the regularity of the free boundary in two-phase problems for linear elliptic operators started in [M.C. Cerutti, F. Ferrari, S. Salsa, Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are C^{1,gamma} [Arch. Ration. Mech. Anal. 171 (2004) 329–348]. In particular we prove that Lipschitz and flat free boundaries (in a suitable sense) are smooth. As byproduct, we prove that Lipschitz free boundaries are smooth in the case of quasilinear operators of the form div(A(x,u)grad(u)) with Lipschitz coefficients.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
