Boundedness of the extremal solution for semilinear elliptic problems

Dong Ye; Feng Zhou

doi:10.1142/S0219199702000701

Boundedness of the extremal solution for semilinear elliptic problems

Dong Ye, Feng Zhou

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We investigate here the boundedness of extremal solutions for some semilinear elliptic equation -Δu = λf(u) posed on a bounded smooth domain of ℝ^N with Dirichlet boundary condition. Some sufficient conditions for f are established to ensure the regularity of extremal solutions when N ≤ 9, which cover all well-known cases.

Original language	English
Pages (from-to)	547-558
Number of pages	12
Journal	Communications in Contemporary Mathematics
Volume	4
Issue number	3
DOIs	https://doi.org/10.1142/S0219199702000701
State	Published - Aug 2002

Keywords

Extremal solution
Regularity
Semilinear elliptic equation

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10.1142/S0219199702000701

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title = "Boundedness of the extremal solution for semilinear elliptic problems",

abstract = "We investigate here the boundedness of extremal solutions for some semilinear elliptic equation -Δu = λf(u) posed on a bounded smooth domain of ℝN with Dirichlet boundary condition. Some sufficient conditions for f are established to ensure the regularity of extremal solutions when N ≤ 9, which cover all well-known cases.",

keywords = "Extremal solution, Regularity, Semilinear elliptic equation",

author = "Dong Ye and Feng Zhou",

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AU - Ye, Dong

AU - Zhou, Feng

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N2 - We investigate here the boundedness of extremal solutions for some semilinear elliptic equation -Δu = λf(u) posed on a bounded smooth domain of ℝN with Dirichlet boundary condition. Some sufficient conditions for f are established to ensure the regularity of extremal solutions when N ≤ 9, which cover all well-known cases.

AB - We investigate here the boundedness of extremal solutions for some semilinear elliptic equation -Δu = λf(u) posed on a bounded smooth domain of ℝN with Dirichlet boundary condition. Some sufficient conditions for f are established to ensure the regularity of extremal solutions when N ≤ 9, which cover all well-known cases.

KW - Extremal solution

KW - Regularity

KW - Semilinear elliptic equation

UR - https://www.scopus.com/pages/publications/0036692518

U2 - 10.1142/S0219199702000701

DO - 10.1142/S0219199702000701

M3 - 文章

AN - SCOPUS:0036692518

SN - 0219-1997

VL - 4

SP - 547

EP - 558

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 3

ER -

Boundedness of the extremal solution for semilinear elliptic problems

Abstract

Keywords

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