Quadrature Domains and p-Laplacian Growth

被引：0
|
作者：
John R. King
Scott W. McCue
机构：
[1] University of Nottingham,School of Mathematical Sciences
[2] Queensland University of Technology,School of Mathematical Sciences
来源：
Complex Analysis and Operator Theory | 2009年 / 3卷
关键词：
Primary 35R35; Secondary 35B40, 76D27; Quadrature domains; -Laplacian; Hele–Shaw flow; Baiocchi transform; moving boundary problem; formal asymptotics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The classical Hele–Shaw (Laplacian-growth) problem is generalised to power-law fluids (satisfying the p-Laplace equation) and a number of results are established that are analogous to some of those involving null-quadrature domains in the former. The results are formal, but suggest a number of avenues warranting rigorous investigation; some of these are formulated as conjectures or open problems.
引用
收藏
页码：453 / 469
页数：16
相关论文
共 50 条
  • [31] Hardy-Lane-Emden inequalities for p-Laplacian on arbitrary domains
    Nguyen Ngoc Trong
    Bui Le Trong Thanh
    Tan Duc Do
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2022, 29 (05):
  • [32] The Brezis-Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains
    Shen, Yan Sheng
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2023, 39 (11) : 2181 - 2206
  • [33] A reiterated homogenization problem for the p-Laplacian equation in corrugated thin domains
    Nakasato, Jean Carlos
    Pereira, Marcone Correa
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 392 : 165 - 208
  • [34] Positive solutions for the p-Laplacian with Robin boundary conditions on irregular domains
    Drabek, P.
    Schindler, I.
    [J]. APPLIED MATHEMATICS LETTERS, 2011, 24 (04) : 588 - 591
  • [35] NONEXISTENCE AND GROWTH OF SOLUTIONS FOR A PARABOLIC p-LAPLACIAN SYSTEM
    Piskin, Erhan
    Ekinci, Fatma
    [J]. SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, 2019, 10 (03): : 301 - 307
  • [36] Variations on the p-Laplacian
    Kawohl, Bernd
    [J]. NONLINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS, 2011, 540 : 35 - 46
  • [37] On the eigenvectors of p-Laplacian
    Luo, Dijun
    Huang, Heng
    Ding, Chris
    Nie, Feiping
    [J]. MACHINE LEARNING, 2010, 81 (01) : 37 - 51
  • [38] Bounce on a p-Laplacian
    Mugnai, D
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2003, 2 (03) : 371 - 379
  • [39] On the eigenvectors of p-Laplacian
    Dijun Luo
    Heng Huang
    Chris Ding
    Feiping Nie
    [J]. Machine Learning, 2010, 81 : 37 - 51
  • [40] The range of the p-Laplacian
    Binding, PA
    Drabek, P
    Huang, YX
    [J]. APPLIED MATHEMATICS LETTERS, 1997, 10 (06) : 77 - 82
12345