# American Institute of Mathematical Sciences

November  2018, 17(6): 2309-2328. doi: 10.3934/cpaa.2018110

## Extremal functions of Moser-Trudinger inequality involving Finsler-Laplacian

 School of Mathematical Sciences, Shanghai Jiao Tong University, 200240, Shanghai, China

* Corresponding author

Received  May 2017 Revised  January 2018 Published  June 2018

Fund Project: The authors are supported partially by NSFC grant No. 11271253 and No. 11771285.

In this paper, we investigate the Moser-Trudinger inequality when it involves a Finsler-Laplacian operator that is associated with functionals containing $F^2(\nabla u)$. Here $F$ is convex and homogeneous of degree 1, and its polar $F^o$ represents a Finsler metric on $\mathbb{R}^n$. We obtain an existence result on the extremal functions for this sharp geometric inequality.

Citation: Changliang Zhou, Chunqin Zhou. Extremal functions of Moser-Trudinger inequality involving Finsler-Laplacian. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2309-2328. doi: 10.3934/cpaa.2018110
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