The infinity-Laplacian in smooth convex domains and in a square-Reference-Cited by-同舟云学术

The infinity-Laplacian in smooth convex domains and in a square

Published:2023 Issue:4 Volume:5 Page:1-16
ISSN:2640-3501
Container-title:Mathematics in Engineering
language:
Short-container-title:MINE

Author:

Brustad Karl K.¹,Lindgren Erik²,Lindqvist Peter³

Affiliation:

1. Frostavegen 1691, NO–7633 Frosta, Norway

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

3. Department of Mathematical Sciences, Norwegian University of Science and Technology, NO–7491, Trondheim, Norway

Abstract

<abstract><p>We extend some theorems for the infinity-ground state and for the infinity-potential, known for convex polygons, to other domains in the plane, by applying Alexandroff's method to the curved boundary. A recent <italic>explicit</italic> solution disproves a conjecture.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Mathematical Physics,Analysis

Reference28 articles.

1. G. Aronsson, Extension of functions satisfying Lipschitz conditions, Ark. Mat., 6 (1967), 551–561. http://doi.org/10.1007/BF02591928

2. G. Aronsson, On the partial differential equation $u_x^2u_xx + 2 u_xu_y u_xy + u_y^2u_yy = 0$, Ark. Mat., 7 (1968), 397–425. http://doi.org/10.1007/BF02590989

3. T. Bhattacharya, E. DiBenedetto, J. Manfredi, Limits as $p \to \infty$ of $\Delta_{p} u = f$ and related extremal problems, Rend. Semin. Mat., Univ. Politec. Torino, 47 (1989), 15–68.

4. F. Bozorgnia, L. Bungert, D. Tenbrinck, The infinity Laplacian eigenvalue problem: reformulation and a numerical scheme, arXiv: 2004.08127.

5. K. K. Brustad, The infinity-potential in the square, arXiv: 2210.03447v2.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Infinity Laplacian Eigenvalue Problem: Reformulation and a Numerical Scheme;Journal of Scientific Computing;2024-01-04

2. The convergence rate of p -harmonic to infinity-harmonic functions;Communications in Partial Differential Equations;2023-11-30