Solutions with interior bubble and boundary layer for an elliptic problem

Liping Wang; Juncheng Wei

doi:10.3934/dcds.2008.21.333

Solutions with interior bubble and boundary layer for an elliptic problem

Liping Wang^*, Juncheng Wei

^*Corresponding author for this work

Chinese University of Hong Kong

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

6 Scopus citations

Abstract

We study positive solutions of the equation ε² Δu -u + u ^n+2/n-2 = 0, where n = 3,4,5, and ε > 0 is small, with Neumann boundary condition in a smooth bounded domain Ω ⊂ R ⁿ. We prove that, along some sequence {ε_j} with ε_j -→ 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂Ω.

Original language	English
Pages (from-to)	333-351
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	21
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2008.21.333
State	Published - May 2008
Externally published	Yes

Keywords

Blow up
Critical sobolev exponent
Semilinear elliptic problem

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title = "Solutions with interior bubble and boundary layer for an elliptic problem",

abstract = "We study positive solutions of the equation ε2 Δu -u + u n+2/n-2 = 0, where n = 3,4,5, and ε > 0 is small, with Neumann boundary condition in a smooth bounded domain Ω ⊂ R n. We prove that, along some sequence \{εj\} with εj -→ 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂Ω.",

keywords = "Blow up, Critical sobolev exponent, Semilinear elliptic problem",

author = "Liping Wang and Juncheng Wei",

year = "2008",

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AU - Wei, Juncheng

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AB - We study positive solutions of the equation ε2 Δu -u + u n+2/n-2 = 0, where n = 3,4,5, and ε > 0 is small, with Neumann boundary condition in a smooth bounded domain Ω ⊂ R n. We prove that, along some sequence {εj} with εj -→ 0, there exists a solution with an interior bubble at an innermost part of the domain and a boundary layer on the boundary ∂Ω.

KW - Blow up

KW - Critical sobolev exponent

KW - Semilinear elliptic problem

UR - https://www.scopus.com/pages/publications/44449086513

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DO - 10.3934/dcds.2008.21.333

M3 - 文章

AN - SCOPUS:44449086513

SN - 1078-0947

VL - 21

SP - 333

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 1

ER -

Solutions with interior bubble and boundary layer for an elliptic problem

Abstract

Keywords

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