2 problems

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Alvino–Ferone–Trombetti conjecture on extremal functions for Hardy–Sobolev–Maz'ya inequalities
Alvino–Ferone–Trombetti's conjecture. Every extremal function $u$ for inequality (1.1) is of the form
Conjectureopenextremal-functions hardy-sobolev-mazya-inequalities symmetryarXiv posted 2 days ago
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Lu–Yang conjecture on sharp Poincaré-Sobolev and Hardy-Sobolev-Maz'ya constants
Let $n\geq 9$ be odd and set $k=\frac{n-1}{2}$ . Denote by $S_{n,k}$ the Sobolev constant, and consider the sharp constants in the Poincaré-Sobolev and Hardy-Sobolev-Maz'ya inequali…
Conjectureopenhardy-sobolev-mazya-inequalities hyperbolic-geometry poincare-sobolev-inequalitiesarXiv posted 2 days ago

Alvino–Ferone–Trombetti conjecture on extremal functions for Hardy–Sobolev–Maz'ya inequalities