Rupert L. Frank

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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…

math.AP2025

Openness of shape optimizers in higher-order and non-scalar problems

Rupert L. Frank

We consider the first eigenvalues of the polyharmonic, LamÃ© and Stokes operators with Dirichlet boundary conditions on sets of given finite measure. It is shown that a quasi-open…

math.AP2024

Minimizing SchrÃ¶dinger eigenvalues for confining potentials

Rupert L. Frank

We consider the problem of minimizing the lowest eigenvalue of the SchrÃ¶dinger operator $- I^ + V$ in $L^{2} (R^{d})$ when the integral $\int e^{- t V} d x$ is given for some $t > 0$ .…