On the number of Courant-sharp Dirichlet eigenvalues

arxiv: 1602.08376 · v3 · pith:QBO456XWnew · submitted 2016-02-26 · 🧮 math.SP · math.AP

On the number of Courant-sharp Dirichlet eigenvalues

Michiel van den Berg , Katie Gittins This is my paper

classification 🧮 math.SP math.AP

keywords courant-sharpdirichletomegaeigenvaluesnumberarbitraryboundsconsider

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We consider arbitrary open sets $\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of $\Omega$. This extends recent results of P. B\'erard and B. Helffer.

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On the number of Courant-sharp Dirichlet eigenvalues

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