Minimising Dirichlet eigenvalues on cuboids of unit measure
classification
🧮 math.SP
keywords
cuboidsmeasureunitdirichleteigenvaluesconsiderconvergescube
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We consider the minimisation of Dirichlet eigenvalues $\lambda_k$, $k \in \N$, of the Laplacian on cuboids of unit measure in $\R^3$. We prove that any sequence of optimal cuboids in $\R^3$ converges to a cube of unit measure in the sense of Hausdorff as $k \rightarrow \infty$.
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