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Lp estimates and asymptotic behavior of extremal function to Hardy-Sobolev type inequality on the H-type group*

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Bulletin of the Brazilian Mathematical Society, New Series Aims and scope Submit manuscript

Abstract.

This paper is devoted to discuss the regularity of the weak solution to a class of non-linear equations corresponding to Hardy-Sobolev type inequality on the H-type group. Combining the Serrin's idea and the Moser's iteration, Lp estimates of the weak solution are obtained, which generalize the results of Garofalo and Vassilev in [6, 14]. As an application, asymptotic behavior of the weak solution has been discussed. Finally, doubling property and unique continuation of the weak solution are given.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, China Jiliang University, Hangzhou, 310018, P.R. CHINA

    Yazhou Han & Shutao Zhang

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  1. Yazhou Han
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  2. Shutao Zhang
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Correspondence to Yazhou Han.

Additional information

*This material is based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y606144.

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Han, Y., Zhang, S. Lp estimates and asymptotic behavior of extremal function to Hardy-Sobolev type inequality on the H-type group*. Bull Braz Math Soc, New Series 38, 437–454 (2007). https://doi.org/10.1007/s00574-007-0054-1

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  • DOI: https://doi.org/10.1007/s00574-007-0054-1

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