3 problems

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Convexity conjecture for uniqueness of Dirichlet fractional problems
Let $a9$ be a bounded domain, and consider problem … . The conjecture proposes a domain-geometric condition extending the known uniqueness result for balls; a general characterizat…
Conjectureopendomain-geometry elliptic-equations fractional-laplacianarXiv posted 2 days ago
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Ramm–Shivakumar conjecture on the first Dirichlet eigenvalue of eccentric annuli
Let $B_r$ and $B_s$ be open disks in $\mathbb{R}^2$ of radii $r$ and $s$ , respectively, with $B_s$ contained in $B_r$ . Let $\lambda_1(B_r\setminus\overline{B_s})$ denote the first…
Conjecturesolveddomain-geometry eigenvalues p-laplacianarXiv posted 2 days ago
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Conjecture on Grad's number near axial symmetry
Conjecture on Grad's number. As the domain $\Omega$ approaches axial symmetry, Grad's number tends to zero:
Conjectureopendomain-geometry functional-analysis korn-inequalityarXiv posted 2 days ago

Convexity conjecture for uniqueness of Dirichlet fractional problems