Sharp Hardy-Leray inequality for curl-free fields with a remainder term |
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Authors: | Naoki Hamamoto Futoshi Takahashi |
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Affiliation: | Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan |
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Abstract: | In this paper, we give a new and a simpler approach to the result in [8] concerning the best constant of Hardy-Leray inequality for curl-free fields. As a by-product, we obtain an improved inequality with a remainder term. The non-attainability of the best constant is an easy consequence of the new inequality. The proof is based on a decomposition of curl-free fields into radial and spherical parts. |
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Keywords: | Hardy-Leray inequality Curl-free vector fields Remainder term The best constant |
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