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math.FA2026

Existence of extremal functions in higher-order affine Sobolev inequalities

Tristan Bullion-Gauthier

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…

math.FA2025

Higher-order affine Sobolev inequalities

Tristan Bullion-Gauthier

Zhang refined the classical Sobolev inequality $∥ f ∥_{L^{N p / (N - p)}} ≲ ∥\nabla f ∥_{L^{p}}$ , where $1 \leq p < N$ , by replacing $∥\nabla f ∥_{L^{p}}$ with a smaller quantit…