4 problems

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Universal leading-order conjecture for the capacitance of thin patches
Let $\Gamma$ be a thin patch obtained by thickening a planar curve by width $2a$ , and let $\mu_0$ denote the quantity appearing in the bounds for the reactive capacitance, with…
Conjectureopenasymptotic-analysis reactive-capacitance thin-domainsarXiv posted 2 days ago
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Sharp $\delta^{1/2}$ convergence rate for thin-domain Reissner\Mindlin systems
Let $(A_\delta)_\delta$ be the family of non-negative self-adjoint operators associated with the ReissnerMindlin system on thin domains $\Omega_\delta$ , and let…
Conjectureopenreissner-mindlin-systems spectral-convergence thin-domainsarXiv posted 2 days ago
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Conjecture on matching asymptotics of Korn inequality constants in thin domains
Matching-asymptotics conjecture. The optimal constants $C_I$ and $C_{II}$ have the same asymptotics as $h$ goes to zero.
Conjectureopenkorn-inequalities thin-domainsarXiv posted 2 days ago
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Conjecture on the first eigenvalues of the Laplacian on a thin planar domain
Let $\Omega_\varepsilon$ be the thin planar domain considered in the paper, let $-\Delta_{\Omega_\varepsilon}^D$ denote its Dirichlet Laplacian, and let $\lambda_{1,m}$ be the eige…
Conjectureopendirichlet-laplacian spectral-theory thin-domainsarXiv posted 2 days ago

Universal leading-order conjecture for the capacitance of thin patches