Abstract
In this paper we introduce and investigate the so-called BV capacity on the generalized Grushin plane \(\mathbb {G}^2_\alpha \), thereby discovering some sharp trace and BV isocapacity inequalities on \(\mathbb {G}^2_\alpha \).
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Acknowledgments
The author is greatly indebted to the referees for their very careful reading and many valuable comments on this paper. The author would like to thank Prof. Jie Xiao for his constructive suggestions and providing his manuscript on this subject. Moreover, the author would like to thank the Department of Mathematics and Statistics at Memorial University of Newfoundland for its hospitality. The author is supported by the National Natural Science Foundation of China (Nos. 10901018, 11471018), the Fundamental Research Funds for the Central Universities (No. FRF-TP-14-005C1), Program for New Century Excellent Talents in University and the Beijing Natural Science Foundation under Grant (No. 1142005).
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Liu, Y. BV Capacity on Generalized Grushin Plane. J Geom Anal 27, 409–441 (2017). https://doi.org/10.1007/s12220-016-9685-z
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DOI: https://doi.org/10.1007/s12220-016-9685-z