# name
Regularity of Lipschitz free boundaries in the alt-Caffarelli problem

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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024.  Director: Xavier Ros

# metadata.dc.description.abstract[].value
In this work we study the regularity of Lipschitz free boundaries in the Alt-Caffarelli problem. We prove that Lipschitz free boundaries are $C^{1, \alpha}$ by exploiting the rescaling invariance of the problem and the initial Lipschitz regularity of the boundary. Moreover, we also show that $C^{1, \alpha}$ boundaries are smooth, which combined with the previous result implies that Lipschitz free boundaries are smooth.

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cc by-nc-nd (c) Joan Domingo Pasarin, 2024

# metadata.dc.title[].value
Regularity of Lipschitz free boundaries in the alt-Caffarelli problem