3 problems

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Uniqueness conjecture for fractional Hardy ground states with a single pole
Uniqueness conjecture. Every positive solution of the single-pole problem is, up to a rescaling, one of the functions $\varphi^\lambda_\mu$ ; these rescalings remain solutions and m…
Conjectureopencritical-elliptic-equations fractional-laplacian hardy-inequalityarXiv posted 2 days ago
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Critical-exponent conjecture for local and global solvability of the semilinear heat equation
Critical-exponent conjecture. The numbers $1+\frac{2}{\alpha}$ and $\frac{Q-\alpha}{Q-2-\alpha}$ are the critical exponents for local and global existence of a weak solution of $$,…
Conjectureopenhardy-inequality semilinear-heat-equations stratified-lie-groupsarXiv posted 2 days ago
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Wang–Ye Hardy–Moser–Trudinger conjecture for bounded convex planar domains
Wang–Ye's Hardy–Moser–Trudinger conjecture. There exists a finite constant $C(\Omega)>0$ such that
Conjectureopenconvex-domains hardy-inequality trudinger-moser-inequalityarXiv posted 2 days ago

Uniqueness conjecture for fractional Hardy ground states with a single pole