二维非线性 Neumann 问题的锐边界集中 *

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-09-10 DOI:10.1088/1361-6544/ad7450

Francesca De Marchis, Habib Fourti and Isabella Ianni

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引用次数: 0

摘要

我们考虑了受非线性诺依曼边界条件限制的有界光滑域中的椭圆方程，并研究了满足均匀能量约束的正解群的指数渐近行为。我们证明了能量量化并描述了边界集中的特征。特别是，我们描述了每个集中点周围解的局部渐近剖面，并得到了-规范的尖锐收敛结果。

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Sharp boundary concentration for a two-dimensional nonlinear Neumann problem *

We consider the elliptic equation in a bounded, smooth domain subject to the nonlinear Neumann boundary condition on and study the asymptotic behaviour as the exponent of families of positive solutions up satisfying uniform energy bounds. We prove energy quantisation and characterise the boundary concentration. In particular we describe the local asymptotic profile of the solutions around each concentration point and get sharp convergence results for the -norm.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.