Quantitative stability for the fractional Hardy inequality is established via localized Poincaré-Sobolev inequalities, Lorentz embeddings, and Emden-Fowler analysis for the p=2 case, yielding a new nonlocal Hardy-Heisenberg uncertainty principle.
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An isoperimetric inequality for level sets in fractional Sobolev spaces is proven and applied to obtain Hölder regularity in fractional De Giorgi classes.
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Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis
Quantitative stability for the fractional Hardy inequality is established via localized Poincaré-Sobolev inequalities, Lorentz embeddings, and Emden-Fowler analysis for the p=2 case, yielding a new nonlocal Hardy-Heisenberg uncertainty principle.
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A fractional De Giorgi isoperimetric type inequality
An isoperimetric inequality for level sets in fractional Sobolev spaces is proven and applied to obtain Hölder regularity in fractional De Giorgi classes.