Boundary-layers for a Neumann problem at higher critical exponents

2016/04/10 by Manna, Bhakti B., Pistoia, Angela
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.02744

Abstract

We consider the Neumann problem (P) - Δv + v= v^q-1 in D, v gt; 0 in D, ∂_νv = 0 on \partialD , where D is an open bounded domain in ℝ^N, 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 \mathcal D, problem (P) has a solution which blows-up along a h-dimensional minimal submanifold of the boundary ∂\mathcal D as q approaches from either below or above the higher critical Sobolev exponent 2(N-h)\over N-h-2.

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