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MiS Preprint

On the Anisotropic Moser-Trudinger inequality for unbounded domains in $\mathbb{R}^{n}$

Changliang Zhou and Chunqin Zhou


In this paper, we investigate a sharp Moser-Trudinger inequality which involves the anisotropic Sobolev norm in unbounded domains. Under this anisotropic Sobolev norm, we establish the Lions type concentration-compactness alternative firstly. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality. In particular, we combine the low dimension case of $n=2$ and the high dimension case of $n\geq 3$ to prove the existence of the extremal functions, which is different from the arguments of isotropic case.

Aug 29, 2019
Sep 2, 2019
moser-trudinger inequality, Anisotropic Sobolev norm, Blow up analysis

Related publications

2020 Repository Open Access
Changliang Zhou and Chunqin Zhou

On the anisotropic Moser-Trudinger inequality for unbounded domains in \(\mathbb {R}^n\)

In: Discrete and continuous dynamical systems / A, 40 (2020) 2, pp. 847-881