STABILITY FOR A GNS INEQUALITY AND THE LOG-HLS INEQUALITY, WITH APPLICATION TO THE CRITICAL MASS KELLER-SEGEL EQUATION
STABILITY FOR A GNS INEQUALITY AND THE LOG-HLS INEQUALITY, WITH APPLICATION TO THE CRITICAL MASS KELLER-SEGEL EQUATION
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DOI：
10.1215/00127094-2019931
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发表时间：
2013-02-15
影响因子：
2.5
通讯作者：
Figalli, Alessio
中科院分区：
文献类型：
--
作者：
Carlen, Eric A.;Figalli, Alessio
从Bianchi和Egnell对2-Sobolev不等式的定量稳定性结果出发，我们推导了平面上Gagliardo-Nirenberg-Sobolev不等式的几种不同稳定性结果。然后，利用该不等式与快速扩散方程之间的联系，我们得到了对数Hardy-Littlewood-Sobolev （Log-HLS）不等式的稳定性。最后，利用所有这些估计，我们证明了临界质量Keller-Segel系统的一个定量收敛结果。
Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev (GNS) inequality in the plane. Then, exploiting the connection between this inequality and a fast diffusion equation, we get stability for the logarithmic Hardy-Littlewood-Sobolev (Log-HLS) inequality. Finally, using all these estimates, we prove a quantitative convergence result for the critical mass Keller-Segel system.