Boundary-layers for a Neumann problem at higher critical exponents

被引：2
|
作者：
Manna B.B. [1 ]
Pistoia A. [2 ]
机构：
[1] Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior C.U., México D.F.
[2] Dipartimento di Metodi e Modelli Matematici, Università di Roma la Sapienza, via Antonio Scarpa 16, Rome
来源：
Bollettino dell'Unione Matematica Italiana | 2017年 / 10卷 / 3期
关键词：
Blowing-up solutions; Boundary layer; Supercritical problem;
D O I：
10.1007/s40574-016-0108-7
中图分类号：
学科分类号：
摘要：
We consider the Neumann problem -∇ν + ν = νq-1 in D, ν>0 in D, ∂νv =0 on ∂D, (P) where D is an open bounded domain in RN, ν is the unit inner normal at the boundary and q > 2. For any integer, 1 ≤ h ≤ N - 3, we show that, in some suitable domains D,problem (P) has a solution which blows-up along a h-dimensional minimal submanifold of the boundary ∂D as q approaches from either below or above the higher critical Sobolev exponent 2(N-h)/N-h-2. © 2016 Unione Matematica Italiana.
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页码：355 / 368
页数：13
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