Degenerate constants in degree inequalities for Sobolev circle maps: on some problems posed by Brezis

Xu'an Dou, Zeyu Jin

We sharpen the constants in two degree inequalities for circle-valued Sobolev maps in degenerate regimes, as $p\to 1^{+}$ or $\delta \to 0^{+}$. The two proofs use the same power trick toge…