Rupert L. Frank

activity

20102025

most citedEigenvalue bounds for Schrödinger operators with complex potentials

144 citations · 163 across the 8 of their papers we have counts for

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4 papers · 1 filter

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.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.AP2024

Minimizing Schrödinger eigenvalues for confining potentials

Rupert L. Frank

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

math.AP2013★ 18 cited

Uniqueness of radial solutions for the fractional Laplacian

Rupert L. Frank, Enno Lenzmann, Luis Silvestre

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian $(- Δ)^{s}$ with $s \in (0, 1)$ for any space dimensions $…