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• W3094126918 abstract "A family of sharp Lp Sobolev inequalities is established by averaging the length of i-dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical Lp Sobolev inequality of Aubin and Talenti and that the strongest member of this family is the only affine invariant one among them-the affine Lp Sobolev inequality of Lutwak, Yang, and Zhang. When p=1 , the entire family of new Sobolev inequalities is extended to functions of bounded variation to also allow for a complete classification of all extremal functions in this case." @default.
• W3094126918 created "2020-10-29" @default.
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• W3094126918 date "2020-10-24" @default.
• W3094126918 modified "2023-10-12" @default.
• W3094126918 title "Sharp Sobolev Inequalities via Projection Averages" @default.
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• W3094126918 doi "https://doi.org/10.1007/s12220-020-00544-6" @default.
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