Extremal functions for a class of trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary | Zendy

Mengjie Zhang | Zendy

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Extremal functions for a class of trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary

Author(s) -

Mengjie Zhang

Publication year - 2021

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2021038

Subject(s) - mathematics , nabla symbol , combinatorics , boundary (topology) , infimum and supremum , sigma , algebra over a field , omega , pure mathematics , mathematical analysis , physics , quantum mechanics

In this paper, we concern trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary. This kind of inequalities were extensively studied by Osgood-Phillips-Sarnak [24], Liu [20], Li-Liu [17], Yang [31, 32] and others. We establish several trace Trudinger-Moser inequalities and obtain the corresponding extremals via the method of blow-up analysis. The results in the current paper generalize those of Li-Liu [17] and Yang [32, 33].

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