A Trudinger-Moser inequality involving L^p -norm on a closed Riemann surface

Mengjie Zhang

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arXiv · 1911.07299

A Trudinger-Moser inequality involving L^p -norm on a closed Riemann surface

Mengjie Zhang

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Abstract

In this paper, using the method of blow-up analysis, we obtained a Trudinger-Moser inequality involving L p -norm on a closed Riemann surface and proved the existence of an extremal function for the corresponding Trudinger-Moser functional. This extends an early result of Yang [27]. Similar result in the Euclidean space was also established by Lu-Yang [17].

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Mengjie Zhang. 2019-11-13. A Trudinger-Moser inequality involving L^p -norm on a closed Riemann surface. https://arxiv.org/abs/1911.07299

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