HARDY-SOBOLEV INEQUALITIES WITH GENERAL WEIGHTS AND REMAINDER TERMS |
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| Authors: | Chen Zhihui Shen Yaotian |
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| Institution: | [1]School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China [2]Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature. |
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| Keywords: | Hardy-Sobolev inequality general weight best constant |
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