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On the Anisotropic Moser-Trudinger inequality for unbounded domains in
Changliang Zhou and Chunqin Zhou
Abstract
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
- Received:
- 29.08.19
- Published:
- 02.09.19
- Keywords:
- moser-trudinger inequality, Anisotropic Sobolev norm, Blow up analysis