Antonios D. Melas scite author profile

Abstract. Let λ k (Ω) be the kth Dirichlet eigenvalue of a bounded domain Ω in R n . According to Weyl's asymptotic formula we haveThe optimal in view of this asymptotic relation lower estimate for the sums k j=1 λ j (Ω) has been proven by P.Li and S.T.Yau (Comm. Math. Phys. 88 (1983), 309-318). Here we will improve this estimate by adding to its righthand side a term of the order of k that depends on the ratio of the volume to the moment of inertia of Ω.

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On the nodal line of the second eigenfunction of the Laplacian in $\mathbf{R}^2$

Melas¹

1992

J. Differential Geom.

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Antonios D. Melas

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On the nodal line of the second eigenfunction of the Laplacian in $\mathbf{R}^2$

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