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Sobolev type embedding and weak solutions with a prescribed singular set

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Abstract

New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.

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Authors and Affiliations

  1. Department of Mathematics, Henan Normal University, Xinxiang, 453007, China

    ZongMing Guo, XiaoHong Guan & FangShu Wan

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  1. ZongMing Guo
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  2. XiaoHong Guan
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  3. FangShu Wan
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Correspondence to ZongMing Guo.

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Guo, Z., Guan, X. & Wan, F. Sobolev type embedding and weak solutions with a prescribed singular set. Sci. China Math. 59, 1975–1994 (2016). https://doi.org/10.1007/s11425-015-0698-0

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  • DOI: https://doi.org/10.1007/s11425-015-0698-0

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