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Existence and regularity of solutions to semi-linear Dirichlet problem of infinitely degenerate elliptic operators with singular potential term

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Abstract

In this paper, we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term. By using the logarithmic Sobolev inequality and Hardy’s inequality, the existence and regularity of multiple nontrivial solutions have been proved.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Hua Chen, Peng Luo & ShuYing Tian

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  1. Hua Chen
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  2. Peng Luo
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  3. ShuYing Tian
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Correspondence to Hua Chen.

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Chen, H., Luo, P. & Tian, S. Existence and regularity of solutions to semi-linear Dirichlet problem of infinitely degenerate elliptic operators with singular potential term. Sci. China Math. 56, 687–706 (2013). https://doi.org/10.1007/s11425-013-4588-y

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  • DOI: https://doi.org/10.1007/s11425-013-4588-y

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