This article proves the existence of extremal functions in higher-order affine Sobolev inequalities, indicating potential new methods for analysis.
In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces of arbitrary regularity, might be of independent interest.
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Tristan Bullion-Gauthier (2026) studied this question.
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