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arXiv · 2412.08616

Minimizing sequences of Sobolev inequalities revisited

Charlotte Dietze·Phan Thành Nam
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Abstract

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-compactness principle, which does not require any refinement of the Sobolev embedding theorem.

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Charlotte Dietze, Phan Thành Nam. 2024-12-11. Minimizing sequences of Sobolev inequalities revisited. https://arxiv.org/abs/2412.08616

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