analysis / Calculus of variations

Brezis's Problems on Degenerate Constants in Degree Inequalities

Two degree inequalities for circle-valued Sobolev maps have constants that degenerate as $p \to 1^+$ or $\delta \to 0^+$. Brezis posed the problem of sharpening them; both are now sharpened, by the same power trick with elementary estimates.

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analysisMay 23, 2026Significance 20/100Registry: unreviewed

Brezis's Problems on Degenerate Constants in Degree Inequalities

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Two degree inequalities for circle-valued Sobolev maps have constants that degenerate as $p \to 1^+$ or $\delta \to 0^+$. Brezis posed the problem of sharpening them; both are now sharpened, by the same power trick with elementary estimates.

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Two degree inequalities for circle-valued Sobolev maps have constants that degenerate as $p \to 1^+$ or $\delta \to 0^+$. Brezis posed the problem of sharpening them; both are now sharpened, by the same power trick with elementary estimates.

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