A minimization problem with free boundary for <i>p</i>-Laplacian weakly coupled system-Reference-Cited by-同舟云学术

A minimization problem with free boundary for p-Laplacian weakly coupled system

Published:2024-01-01 Issue:1 Volume:13 Page:
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Fotouhi Morteza¹,Shahgholian Henrik²

Affiliation:

1. Department of Mathematical Sciences, Sharif University of Technology , 11155-9415 , Tehran , Iran

2. Department of Mathematics, Royal Institute of Technology , 100 44 Stockholm , Sweden

Abstract

Abstract In this article, we consider a weakly coupled

-Laplacian system of a Bernoulli-type free boundary problem, through minimization of a corresponding functional. We prove various properties of any local minimizer and the corresponding free boundary.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/anona-2023-0138/pdf

Reference20 articles.

1. N. E. Aguilera, L.A. Caffarelli, and J. Spruck, An optimization problem in heat conduction, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 14 (1987), no. 3, 355–387.

2. H. W. Alt and L. A. Caffarelli, Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math. 325 (1981), 105–144.

3. H. Wilhelm Alt, L. A. Caffarelli, and A. Friedman, A free boundary problem for quasi-linear elliptic equations, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze 11 (1984), no. 1, 1–44.

4. B. Bennewitz and J. Lewis, On the dimension of p-harmonic measure, Ann. Acad. Sci. Fenn. Math 30 (2005), no. 2, 459–505.

5. L. A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries part ii: Flat free boundaries are Lipschitz, Commun. Pure Appl. Math. 42 (1989), no. 1, 55–78.

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