University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Inequalities between Dirichlet and Neumann eigenvalues in large dimensions

  Browse A-Z

Log in

University Account External (via Google)

🔐 Log In

Information on

Subscribing to talksdetails Finding a talkdetails Adding a talkdetails Disseminating talksdetails Help and Documentationdetails

ℹī¸ Information

Inequalities between Dirichlet and Neumann eigenvalues in large dimensions

Download to your calendar using vCal

  • UserNikolai Filonov (St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences)
  • ClockWednesday 18 March 2026, 14:00-15:00
  • HouseSeminar Room 2, Newton Institute.

If you have a question about this talk, please contact nobody.

GST - Geometric spectral theory and applications

Let $\Omega\subset\mathbb{R}$ be a bounded domain. Denote by $\{\lambda_{k}\}{\infty}$ (resp. $\{\mu{k}\}_{k=1})$ the eigenvalues of the Laplace operator in $\Omega$ with Dirichlet (resp. Neumann) boundary conditions. Introduce notations $\Phi(d,k,\Omega)=\#\{j:\mu_{j}(\Omega)\le\lambda_{k}(\Omega)\}$, $\Psi(d,k,\Omega)=\Phi(d,k,\Omega)-k$ , so the inequality $\mu_{k+\Psi(d,k,\Omega)}\le\lambda_{k}$ holds true. In 1986, Levine and Weinberger proved the estimate $\Psi(d,k,\Omega)\ge d$ for all convex domains. We show that for $d\gg1$ this result can be improved: $\Psi(d,k,\Omega)\ge C(\frac{e}{2}){d}$ also for all convex domains. The similar estimate holds for $k=1$: $\Psi(d,1,\Omega)\ge C(\frac{e}{2})^{d}$ for arbitrary domains.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

Note that ex-directory lists are not shown.

Other lists

Average on Sundays: 7269.89215686 kWh Lecture Theatre, Biochemistry, Department of Keynes Hall

Other talks

Using numerical simulations for solving spectral geometry problems There is no such thing as weather: a historical and cultural geography of weather (and health) TOWARD AFFORDABLE PREVENTIVE HEALTHCARE: How basic science addresses grand challenges External Seminar - Michael Raissig TBC Title to be confirmed Pollution in Helmholtz boundary integral methods
 

Š 2006-2025 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity