144 citations · 163 across the 8 of their papers we have counts for
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math.AP2025
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…
math.SP2025
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…
math.AP2025
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…