Hostname: page-component-f554764f5-8cg97 Total loading time: 0 Render date: 2025-04-13T00:59:27.667Z Has data issue: false hasContentIssue false
  • English
  • Français

Properties of the extremal solution for a fourth-order elliptic problem

Published online by Cambridge University Press:  20 September 2012

Baishun Lai  and
Zhuoran Du
Baishun Lai
Affiliation:
Institute of Contemporary Mathematics, and School of Mathematics and Information Science, Henan University, Kaifeng 475004, People's Republic of China ([email protected])
Zhuoran Du
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, People's Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

Let λ* > 0 denote the largest possible value of λ such that the system

has a solution, where is the unit ball in ℝn centred at the origin, p > 1 and n is the exterior unit normal vector. We show that for λ = λ* this problem possesses a unique weak solution u*, called the extremal solution. We prove that u* is singular when n ≥ 13 for p large enough and actually solve part of the open problem which Dávila et al. left unsolved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 5 , October 2012 , pp. 1051 - 1069
Copyright
Copyright © Royal Society of Edinburgh 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable