Rupert L. Frank

Applied Mathematics · 2007–2022

A researcher in the Science corpus: 18 papers; trusts 58 researchers and is trusted by 59 researchers here, as inferred from the citation graph.

Subfields

• Applied Mathematics — 112 citations into it; #289 of 7,620 by trust here, #204 by citations
• Mathematical Physics — 66 citations into it; #888 of 8,562 by trust here, #421 by citations
• Computational Theory and Mathematics — 39 citations into it; #5,610 of 12,182 by trust here, #5,724 by citations
• Geometry and Topology — 28 citations into it; #3,715 of 7,422 by trust here, #4,440 by citations
• Statistical and Nonlinear Physics — 9 citations into it
• Atomic and Molecular Physics, and Optics — 5 citations into it
• Modeling and Simulation — 5 citations into it
• Numerical Analysis — 5 citations into it

Whom Rupert L. Frank trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Elliott H. Lieb
2. Yanyan Li
3. Robert Seiringer
4. Li Ma
5. X. Cabré
6. Luis Caffarelli
7. Bartłomiej Dyda
8. Vladimir G. Maz'ya
9. Luis Silvestre
10. G. Barbatis

Who trusts Rupert L. Frank overall

1. Bartłomiej Dyda
2. Boumediene Abdellaoui
3. Luz Roncal
4. J. D'avila
5. Lorenzo Brasco
6. William Beckner
7. M. Folz
8. Michael Ruzhansky
9. Krzysztof Bogdan
10. Jingbo Dou

Papers from Rupert L. Frank's perspective

Ordered by how strongly the researchers Rupert L. Frank trusts endorse each paper. Same corpus, a different order for every researcher.

1. Remark on some conformally invariant integral equations: the method of moving spheres
2. Fractional Laplacian in conformal geometry
3. Regularity of the obstacle problem for a fractional power of the laplace operator
4. Nonlinear equations for fractional Laplacians I: Regularity, maximum principles, and Hamiltonian estimates
5. An Extension Problem Related to the Fractional Laplacian
6. A MASS-TRANSPORTATION APPROACH TO SHARP SOBOLEV AND GAGLIARDO-NIRENBERG INEQUALITIES
7. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
8. Non-linear ground state representations and sharp Hardy inequalities
9. A unified approach to improved L p Hardy inequalities with best constants
10. Scattering matrix in conformal geometry

Their papers

• Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality (2009) — 135 citations
• Hardy-Sobolev-Maz'ya inequalities for arbitrary domains (2011) — 50 citations
• Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022) — 75 citations
• Classification of positive solutions to a nonlinear biharmonic equation with critical exponent (2017) — 48 citations
• Maximizers for the Stein–Tomas Inequality (2016) — 57 citations
• Eigenvalue bounds for Schrödinger operators with complex potentials. II (2015) — 157 citations
• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates (2014) — 135 citations
• Uniqueness of Radial Solutions for the Fractional Laplacian (2013) — 597 citations
• An extension problem for the CR fractional Laplacian (2013) — 91 citations
• Remainder terms in the fractional Sobolev inequality (2012) — 137 citations
• Fractional Hardy-Sobolev-Maz'ya inequality for domains (2011) — 58 citations
• Sharp constants in several inequalities on the Heisenberg group (2010) — 230 citations
• Uniqueness of non-linear ground states for fractional Laplacians in $${\mathbb{R}}$$R (2010) — 338 citations
• Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory (2010) — 129 citations
• A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality (2010) — 116 citations
• Sharp Fractional Hardy Inequalities in Half-Spaces (2009) — 63 citations
• Non-linear ground state representations and sharp Hardy inequalities (2008) — 497 citations
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators (2007) — 334 citations