1 citations · 1 across the 4 of their papers we have counts for
5 papers
Openness of shape optimizers in higher-order and non-scalar problems
Rupert L. Frank
We consider the first eigenvalues of the polyharmonic, Lamé and Stokes operators with Dirichlet boundary conditions on sets of given finite measure. It is shown that a quasi-open s…
Eigenvalue lower bounds through a generalized inradius
Rupert L. Frank, Ari Laptev, Durvudkhan Suragan
Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for ei…
Explicit minimisers for anisotropic Riesz energies
Rupert L. Frank, Joan Mateu, Maria Giovanna Mora +3
In this paper we describe explicitly the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisot…
Open problem: Violation of locality for Schrödinger operators with complex potentials
Jean-Claude Cuenin, Rupert L. Frank
We explain in which sense Schrödinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomen…
Eigenvalue bounds for Schrödinger operators with complex potentials. II
Rupert L. Frank, Barry Simon
Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator in with complex potential has absolute value at most a constant…