We consider a one-phase free boundary problem for -Laplacian with non-zero right hand side. We use the approach present in  to prove that flat free boundaries and Lipschitz free boundaries are .
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Raimundo Leitão, Gleydson C. Ricarte, Free boundary regularity for a degenerate problem with right hand side. Interfaces Free Bound. 20 (2018), no. 4, pp. 577–595DOI 10.4171/IFB/413