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Regularity of the free boundary in two-phase problems for linear elliptic operators |
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| Authors: | Fausto Ferrari Sandro Salsa |
| Institution: | a Dipartimento di Matematica dell'Università, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy b C.I.R.A.M., Via Saragozza, 8, 40123 Bologna, Italy c Dipartimento di Matematica del Politecnico, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy |
| 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 C1,γ, 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)∇u) with Lipschitz coefficients. |
| Keywords: | Free boundary Strict ε-monotonicity Two-phase problems Elliptic operators |
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