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Extremals for Fractional Moser–Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates
Advanced Nonlinear Studies ( IF 2.1 ) Pub Date : 2020-08-01 , DOI: 10.1515/ans-2020-2089
Gabriele Mancini 1 , Luca Martinazzi 2
Affiliation  

Abstract We prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained via commutator techniques.

中文翻译:

通过谐波扩展和换向器估计得出的第 1 维分数 Moser-Trudinger 不等式的极值

摘要 我们证明了区间内和整条实线上的分数 Moser-Trudinger 不等式的极值的存在。在这两种情况下,我们都对相应的 Euler-Lagrange 方程使用爆炸分析,这需要通过换向器技术获得新的锐利估计。
更新日期:2020-08-01
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