Regularity of Lipschitz free boundaries in the Alt-Caffarelli problem

Authors

  • Joan Domingo Pasarin

Keywords:

partial differential equations, free boundary problems, Alt– Caffarelli problem, Lipschitz regularity.

Abstract

En aquest treball estudiem la regularitat de les fronteres lliures Lipschitz en el problema d’Alt–Caffarelli. Demostrem que les fronteres lliures Lipschitz són C1,α mitjançant la invariància per reescalament del problema i la regularitat inicial Lipschitz de la frontera. A més a més, també provem que les fronteres C1,α són C∞, cosa que, juntament amb el resultat anterior, implica que les fronteres lliures Lipschitz són C∞.

Downloads

Download data is not yet available.

Downloads

How to Cite

Domingo Pasarin, J. (2024). Regularity of Lipschitz free boundaries in the Alt-Caffarelli problem. Reports@SCM, 9(1), 93–94. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154346

Issue

Vol. 9 No. 1 (2024)

Section

Extended abstracts

License

The intellectual property of articles belongs to the respective authors.
On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:
  1. Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.
  2. Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.
  3. Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.
  4. Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.
  5. The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.
  6. The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.