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Poincaré inequalities in weighted Sobolev spaces

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Abstract

The weighted Poincaré inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincaré inequalities hold if, and only if, the ball measure of non-compactness of the natural embedding of weighted Sobolev spaces is less than 1.

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Authors and Affiliations

  1. Department of Mathematics, Inner Mongolia University, Huhhot, 010021, P.R.China

    Wang Wan-yi  (王万义) (Professor, Doctor) & Sun Jiong  (孙炯)

  2. Department of Mathematics, Inner Mongolia Normal University, Huhhot, 010022, P.R.China

    Wang Wan-yi  (王万义) (Professor, Doctor)

  3. School of Mathematical Sciences, Beijing University, Beijing, 100871, P.R.China

    Wang Wan-yi  (王万义) (Professor, Doctor) & Zheng Zhi-ming  (郑志明)

Authors
  1. Wang Wan-yi  (王万义)
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  2. Sun Jiong  (孙炯)
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  3. Zheng Zhi-ming  (郑志明)
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Corresponding author

Correspondence to Wang Wan-yi  (王万义).

Additional information

Project supported by the National Natural Science Foundation of China (Nos.10261004 and 10461006), the Visiting Scholar Foundation of Key Laboratory of University and the Natural Science Foundation of the Inner Mongolia Autonomous Region of China(No.200408020104)

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Wang, Wy., Sun, J. & Zheng, Zm. Poincaré inequalities in weighted Sobolev spaces. Appl Math Mech 27, 125–132 (2006). https://doi.org/10.1007/s10483-006-0116-1

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  • DOI: https://doi.org/10.1007/s10483-006-0116-1

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