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math.AP2024
Minimizing sequences of Sobolev inequalities revisited
Charlotte Dietze, Phan Thành Nam
We give a new proof of the compactness of minimizing sequences of the Sobolev inequalities in the critical case. Our approach relies on a simplified version of the concentration-co…
math.AP2023
Isoperimetric inequalities for inner parallel curves
Charlotte Dietze, Ayman Kachmar, Vladimir Lotoreichik
We prove weighted isoperimetric inequalities for smooth, bounded, and simply connected domains. More precisely, we show that the moment of inertia of inner parallel curves for doma…