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math.SP2016★ 13 cited
Minimising Dirichlet eigenvalues on cuboids of unit measure
Michiel van den Berg, Katie Gittins
We consider the minimisation of Dirichlet eigenvalues , , of the Laplacian on cuboids of unit measure in . We prove that any sequence of optimal cuboids in $\R…
math.SP2016★ 1 cited
On the number of Courant-sharp Dirichlet eigenvalues
Michiel van den Berg, Katie Gittins
We consider arbitrary open sets in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of , (ii) the…