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Creators/Authors contains: "Frank, Rupert_L"

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  1. ; ; (, Letters in Mathematical Physics)
    Abstract We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application, we reprove and extend some theorems about eigenvalue asymptotics of Schrödinger operators with homogeneous potentials. The case of main interest is where the Weyl expression is infinite and a partially semiclassical limit occurs. 
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  2. ; ; (, Partial Differential Equations and Applications)
    Abstract In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains. 
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  3. ; (, Archive for Rational Mechanics and Analysis)
    Abstract We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that in an optimal part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions. 
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  4. ; (, Communications in Mathematical Physics)
    Abstract By the Aharonov–Casher theorem, the Pauli operatorPhas no zero eigenvalue when the normalized magnetic flux$$\alpha $$ α satisfies$$|\alpha |<1$$ | α | < 1 , but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the$$\gamma $$ γ -th moment of the eigenvalues of$$P+V$$ P + V is valid under the optimal restrictions$$\gamma \ge |\alpha |$$ γ ≥ | α | and$$\gamma >0$$ γ > 0 . Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order$$\gamma \ge 1$$ γ ≥ 1 . 
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