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Document type

Master thesis

Publication date

2024-06-27

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cc by-nc-nd (c) Joan Domingo Pasarin, 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216888

Regularity of Lipschitz free boundaries in the alt-Caffarelli problem

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Abstract

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.

Description

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

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Funcions harmòniques, Equacions en derivades parcials, Treballs de fi de màster, Problemes de contorn

Subject (English)

Harmonic functions, Partial differential equations, Master's thesis, Boundary value problems

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Màster Oficial - Matemàtica Avançada

Citation

DOMINGO PASARIN, Joan. Regularity of Lipschitz free boundaries in the alt-Caffarelli problem. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/216888

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