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- W4387561335 abstract "We investigate necessary and sufficient conditions on the weights for the Hardy-Rellich inequalities to hold, and propose a new way to use the notion of Bessel pair to establish the optimal Hardy-Rellich type inequalities. Our results sharpened earlier Hardy-Rellich and Rellich type inequalities in the literature. We also study several results about the symmetry and symmetry breaking properties of the Rellich type and Hardy-Rellich type inequalities, and then partially answered an open question raised by Ghoussoub and Moradifam. Namely, we will present conditions on the weights such that the Rellich type and Hardy-Rellich type inequalities hold for all functions if and only if the same inequalities hold for all radial functions." @default.
- W4387561335 created "2023-10-12" @default.
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- W4387561335 date "2023-10-10" @default.
- W4387561335 modified "2023-10-13" @default.
- W4387561335 title "A new approach to weighted Hardy-Rellich inequalities: improvements, symmetrization principle and symmetry breaking" @default.
- W4387561335 doi "https://doi.org/10.48550/arxiv.2310.06637" @default.
- W4387561335 hasPublicationYear "2023" @default.
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