Du, Yihong; Guo, Zongming

Author(s)

Du, Yihong

Guo, Zongming

Publication Date

2004

Abstract

For a wide class of nonlinearities f (u) satisfying f (u) > 0 in (0, a) and f(u) < 0 in (a,∞), but not necessarily Lipschitz continuous, we study the quasi-linear equation -Δ pu = f(u) in T, u│∂T = 0, where T = {x = (x₁,x₂,...., xN )ϵ ℝ^2 RN :x₁ > 0}≽ with N > 2. By using a new approach based on the weak maximum principle, we show that any positive solution on T must be a function of x1 only. Under our assumptions, the strong maximum principle does not hold in general and the solution may develop a flat core; our symmetry result allows an easy and precise determination of the flat core.

Citation

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, 134A(2), p. 259-269

ISSN

1473-7124

0308-2105

Link

https://hdl.handle.net/1959.11/3867

Publisher

The RSE Scotland Foundation

Title

Symmetry for elliptic equations in a half-space without strong maximum principle

Type of document

Journal Article

Entity Type

Publication

Author(s)	Du, Yihong Guo, Zongming
Publication Date	2004
Abstract	For a wide class of nonlinearities f (u) satisfying f (u) > 0 in (0, a) and f(u) < 0 in (a,∞), but not necessarily Lipschitz continuous, we study the quasi-linear equation -Δ pu = f(u) in T, u│∂T = 0, where T = {x = (x₁,x₂,...., xN )ϵ ℝ^2 RN :x₁ > 0}≽ with N > 2. By using a new approach based on the weak maximum principle, we show that any positive solution on T must be a function of x1 only. Under our assumptions, the strong maximum principle does not hold in general and the solution may develop a flat core; our symmetry result allows an easy and precise determination of the flat core.
Citation	Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, 134A(2), p. 259-269
ISSN	1473-7124 0308-2105
Link	https://hdl.handle.net/1959.11/3867
Publisher	The RSE Scotland Foundation
Title	Symmetry for elliptic equations in a half-space without strong maximum principle
Type of document	Journal Article
Entity Type	Publication

Symmetry for elliptic equations in a half-space without strong maximum principle

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