2 problems

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Freitas conjecture on the Dirichlet–Neumann eigenvalue shift
Let $\Omega\subset\mathbb{R}^d$ be a domain, and let $\lambda_j(\Delta_D)$ and $\lambda_j(\Delta_N)$ denote the $j$ -th Dirichlet and Neumann Laplacian eigenvalues. Define … where…
Conjectureopendirichlet-neumann-eigenvalues laplacian spectral-geometryarXiv posted 2 days ago
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Benguria–Levitin–Parnovski conjecture on the Dirichlet–Neumann eigenvalue shift
Let $\Omega\subset\mathbb{R}^d$ be a domain, and let $\lambda_j(\Delta_D)$ and $\lambda_j(\Delta_N)$ denote the $j$ -th Dirichlet and Neumann Laplacian eigenvalues, respectively. Be…
Conjectureopendirichlet-neumann-eigenvalues laplacian spectral-geometryarXiv posted 2 days ago

Freitas conjecture on the Dirichlet–Neumann eigenvalue shift