Blow-up analysis concerning singular Trudinger–Moser inequalities in dimension two

By Y. Yang, Xiaobao Zhu. 2016

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Abstract In this paper, we derive a sharp version of the singular Trudinger–Moser inequality, which was originally established by Adimurthi and Sandeep [2] . Moreover, extremal functions for those singular Trudinger–Moser inequalities are also obtained. Our method is the blow-up analysis. Compared with our previous work ( [32] ), the essential difficulty caused by the presence of singularity is how to analyse the asymptotic behavior of certain maximizing sequence near the blow-up point. We overcome this difficulty by combining two different classification theorems of Chen and Li [6,7] to get the desired bubble.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/765fcab289530527f9f2511cd31a9d7266f60ff4