A Neumann problem with critical exponent in nonconvex domains and Lin-Ni's conjecture

Liping Wang; Juncheng Wei; Shusen Yan

A Neumann problem with critical exponent in nonconvex domains and Lin-Ni's conjecture

Liping Wang
, Juncheng Wei
, Shusen Yan

Mathematics

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

52 Citations (Scopus)

Abstract

In this paper, we consider the nonlinear elliptic Neumann problem... [This] equation arises in many branches of applied science. For example, it can be viewed as a steady-state equation for the shadow system of the Gierer-Meinhardt system in biology pattern formation, or for parabolic equations in chemotaxis, e.g. the Keller-Segel model.

Original language	English
Pages (from-to)	4581-4615
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	9
Publication status	Published - 2010

Keywords

Partial Differential Equations

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title = "A Neumann problem with critical exponent in nonconvex domains and Lin-Ni's conjecture",

abstract = "In this paper, we consider the nonlinear elliptic Neumann problem... [This] equation arises in many branches of applied science. For example, it can be viewed as a steady-state equation for the shadow system of the Gierer-Meinhardt system in biology pattern formation, or for parabolic equations in chemotaxis, e.g. the Keller-Segel model.",

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AB - In this paper, we consider the nonlinear elliptic Neumann problem... [This] equation arises in many branches of applied science. For example, it can be viewed as a steady-state equation for the shadow system of the Gierer-Meinhardt system in biology pattern formation, or for parabolic equations in chemotaxis, e.g. the Keller-Segel model.

KW - Partial Differential Equations

UR - http://www.ams.org/journals/tran/2010-362-09/S0002-9947-10-04955-X/home.html

M3 - Article

SN - 0002-9947

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EP - 4615

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -

A Neumann problem with critical exponent in nonconvex domains and Lin-Ni's conjecture

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