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Interfaces and Free Boundaries


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Volume 20, Issue 4, 2018, pp. 577–595
DOI: 10.4171/IFB/413

Published online: 2018-12-13

Free boundary regularity for a degenerate problem with right hand side

Raimundo Leitão[1] and Gleydson C. Ricarte[2]

(1) Universidade Federal do Ceará, Fortaleza, Brazil
(2) Universidade Federal do Ceará, Fortaleza, Brazil

We consider a one-phase free boundary problem for $p$-Laplacian with non-zero right hand side. We use the approach present in [6] to prove that flat free boundaries and Lipschitz free boundaries are $C^{1, \gamma}$.

Keywords: Free boundary problems, degenerate elliptic operators, regularity theory

Leitão Raimundo, Ricarte Gleydson: Free boundary regularity for a degenerate problem with right hand side. Interfaces Free Bound. 20 (2018), 577-595. doi: 10.4171/IFB/413