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Blow-up analysis in dimension 2 and a sharp form of Trudinger-Moser inequality

机译：2维的爆炸分析和Trudinger-Moser不等式的尖锐形式

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This paper deals with an improvement of the Trudinger-Moser inequality associated to the embedding of the standard Sobolev space H-0(1)(Omega) into Orlicz spaces for Omega a smooth bounded domain in R-2. The inequality proved here gives in particular precise informations on a previous result obtained by Lions and can be very useful in the study of lack of compactness of the embedding of H-0(1)(Omega) into {exp(4piu(2)) is an element of L-1(Omega)}. We also provide a general asymptotic analysis for sequences of solutions to elliptic PDE's with critical Sobolev growth which blow up at some point. We obtain in particular a result which is well-known in higher dimensions: the concentration points are located at critical points of the regular part of the Green function of the linear operator involved in the equation. [References: 23]
机译：本文处理了与标准Sobolev空间H-0（1）（Omega）嵌入到Orlicz空间相关的Trudinger-Moser不等式的改进，其中O-2是R-2中的光滑有界域。这里证明的不等式给出了Lions先前获得的结果的特别精确的信息，并且在缺乏将H-0（1）（Omega）嵌入{exp（4piu（2））的紧凑性研究中非常有用。是L-1（Ω）的元素}。我们还提供了具有临界Sobolev增长的椭圆PDE解的序列的一般渐近分析，该增长在某个时候会爆炸。我们特别获得了在更高维度上众所周知的结果：集中点位于方程中涉及的线性算子的格林函数Green函数正则部分的临界点。 [参考：23]

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