Abstract
Let \({\mathcal {H}}_{\alpha }=\Delta -(\alpha -1)|x|^{\alpha }\) be an \([1,\infty )\ni \alpha \)-Hermite operator for the hydrogen atom located at the origin in \({\mathbb {R}}^d\). In this paper, we are motivated by the classical case \(\alpha =1\) to investigate the space of functions with \(\alpha \)-Hermite Bounded Variation and its functional capacity and geometrical perimeter.
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Acknowledgements
The authors are grateful for Prof. Jie Xiao for many helpful and useful suggestions. The authors also would like to thank the referee for his valuable comments which improve the presentation of this article. In addition:
\(\bullet \) Jizhen Huang was supported by Fundamental Research Funds for the Central Universities (# 500419772).
\(\bullet \) Pengtao Li was in part supported by National Natural Science Foundation of China (# 11871293 & # 12071272) & Shandong Natural Science Foundation of China (# ZR2017JL008, # ZR2016AM05).
\(\bullet \) Yu Liu was supported by National Natural Science Foundation of China (# 11671031) & Beijing Municipal Science and Technology Project (# Z17111000220000).
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Huang, J., Li, P. & Liu, Y. Capacity & perimeter from \(\alpha \)-Hermite bounded variation. Calc. Var. 59, 186 (2020). https://doi.org/10.1007/s00526-020-01851-0
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DOI: https://doi.org/10.1007/s00526-020-01851-0