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On the behavior of the free boundary for a one-phase Bernoulli problem with mixed boundary conditions

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The authors acknowledge the Center for Nonlinear Analysis (NSF PIRE Grant No. OISE- 0967140) where part of this work was carried out. The research of G. Gravina and G. Leoni was partially funded by the National Science Foundation under Grants No. DMS-1412095 and DMS- 1714098. G. Gravina also acknowledges the support of the research support programs of Charles University: PRIMUS/19/SCI/01 and UNCE/SCI/023

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