<h1>Frank, Rupert</h1>
<h2>Monograph from <a href="https://authors.library.caltech.edu">CaltechAUTHORS</a></h2>
<ul>
<li>Frank, Rupert L. and Gontier, David, el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211018-185313891">Optimizers for the finite-rank Lieb-Thirring inequality</a>; <a href="https://doi.org/10.48550/arXiv.2109.05984">10.48550/arXiv.2109.05984</a></li>
<li>Frank, Rupert L. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211018-185309868">Some minimization problems for mean field models with competing forces</a>; <a href="https://doi.org/10.48550/arXiv.2109.02393">10.48550/arXiv.2109.02393</a></li>
<li>Frank, Rupert L. and Larson, Simon (2021) <a href="https://authors.library.caltech.edu/records/bkex1-ej117">Discrete Schrödinger operators with decaying and oscillating potentials</a>; St. Petersburg Mathematical Journal; Vol. 35; No. 1; 233-244; <a href="https://doi.org/10.1090/spmj/1803">10.1090/spmj/1803</a></li>
<li>Frank, Rupert L. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211018-185230397">Degenerate stability of some Sobolev inequalities</a>; <a href="https://doi.org/10.48550/arXiv.2107.11608">10.48550/arXiv.2107.11608</a></li>
<li>Frank, Rupert L. and Loss, Michael (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211018-185216561">Existence of optimizers in a Sobolev inequality for vector fields</a>; <a href="https://doi.org/10.48550/arXiv.2107.06450">10.48550/arXiv.2107.06450</a></li>
<li>Frank, Rupert L. and Larson, Simon (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211004-232828060">On the spectrum of the Kronig-Penney model in a constant electric field</a>; <a href="https://doi.org/10.48550/arXiv.2104.10256">10.48550/arXiv.2104.10256</a></li>
<li>Frank, Rupert L. and König, Tobias, el al. (2021) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211004-232817904">Blow-up of solutions of critical elliptic equation in three dimensions</a>; <a href="https://doi.org/10.48550/arXiv.2102.10525">10.48550/arXiv.2102.10525</a></li>
<li>Frank, Rupert L. and Larson, Simon (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211004-222658897">Semiclassical asymptotics for a class of singular Schrödinger operators</a>; <a href="https://doi.org/10.48550/arXiv.2010.05417">10.48550/arXiv.2010.05417</a></li>
<li>Frank, Rupert L. and Gontier, David, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211004-222655493">The periodic Lieb-Thirring inequality</a>; <a href="https://doi.org/10.48550/arXiv.2010.02981">10.48550/arXiv.2010.02981</a></li>
<li>Frank, Rupert L. and Merz, Konstantin, el al. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20211004-222648670">Relativistic Strong Scott Conjecture: A Short Proof</a>; <a href="https://doi.org/10.48550/arXiv.2009.02474">10.48550/arXiv.2009.02474</a></li>
<li>Frank, Rupert L. (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200819-122507869">The Lieb-Thirring inequalities: Recent results and open problems</a>; <a href="https://doi.org/10.48550/arXiv.2007.09326">10.48550/arXiv.2007.09326</a></li>
<li>Frank, Rupert L. and Sabin, Julien (2020) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200819-151324737">Sharp Weyl laws with singular potentials</a>; <a href="https://doi.org/10.48550/arXiv.2007.04284">10.48550/arXiv.2007.04284</a></li>
<li>Carlen, Eric A. and Frank, Rupert L., el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190520-141054764">Inequalities for L^p-norms that sharpen the triangle inequality and complement Hanner's Inequality</a>; <a href="https://doi.org/10.48550/arXiv.1807.05599">10.48550/arXiv.1807.05599</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H. (2016) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170428-161302774">A 'liquid-solid' phase transition in a simple model for swarming, based on the 'no flat-spots' theorem for subharmonic functions</a>; <a href="https://doi.org/10.48550/arXiv.1607.07971">10.48550/arXiv.1607.07971</a></li>
<li>Frank, R. L. and Hainzi, C., el al. (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170505-112911639">Microscopic Derivation of the Ginzburg-Landau Model</a>; <a href="https://doi.org/10.48550/arXiv.1209.1080">10.48550/arXiv.1209.1080</a></li>
<li>Frank, Rupert L. and Lenzmann, Enno (2015) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-072727175">Uniqueness and Nondegeneracy of Ground States for (−Δ)^sQ+Q−Q^(α+1)=0 in R</a>; <a href="https://doi.org/10.48550/arXiv.1009.4042">10.48550/arXiv.1009.4042</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H., el al. (2012) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170505-111204119">Ground state properties of multi-polaron systems</a>; <a href="https://doi.org/10.48550/arXiv.1209.3717">10.48550/arXiv.1209.3717</a></li>
<li>Chen, Shibing and Frank, Rupert L., el al. (2012) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170502-150250004">Remainder terms in the fractional Sobolev inequality</a>; <a href="https://doi.org/10.48550/arXiv.1205.5666">10.48550/arXiv.1205.5666</a></li>
<li>Dyda, Bartlomiej and Frank, Rupert L. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-094456500">Fractional Hardy-Sobolev-Maz'ya inequality for domains</a>; <a href="https://doi.org/10.48550/arXiv.1109.6570">10.48550/arXiv.1109.6570</a></li>
<li>Cornean, Horia D. and Fournais, Søren, el al. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-100604320">Sharp trace asymptotics for a class of 2D-magnetic operators</a>; <a href="https://doi.org/10.48550/arXiv.1108.0777">10.48550/arXiv.1108.0777</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H., el al. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-091837793">Binding of Polarons and Atoms at Threshold</a>; <a href="https://doi.org/10.48550/arXiv.1106.0729">10.48550/arXiv.1106.0729</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-082647988">Possible Lattice Distortions in the Hubbard Model for Graphene</a>; <a href="https://doi.org/10.48550/arXiv.1105.0693">10.48550/arXiv.1105.0693</a></li>
<li>Frank, Rupert L. and Lenzmann, Enno (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170526-101905288">On ground states for the L^2-critical boson star equation</a>; <a href="https://doi.org/10.48550/arXiv.0910.2721">10.48550/arXiv.0910.2721</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H., el al. (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-091442211">Müeller's Exchange-Correlation Energy in Density-Matrix-Functional Theory</a>; <a href="https://doi.org/10.48550/arXiv.0705.1587">10.48550/arXiv.0705.1587</a></li>
<li>Frank, Rupert L. and Lenzmann, Enno (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170526-093631237">Uniqueness of ground states for the L^2-critical boson star equation</a>; <a href="https://doi.org/10.48550/arXiv.0905.3105">10.48550/arXiv.0905.3105</a></li>
<li>Frank, Rupert L. (2009) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170526-092635990">Remarks on eigenvalue estimates and semigroup domination</a>; <a href="https://doi.org/10.48550/arXiv.0903.0561">10.48550/arXiv.0903.0561</a></li>
<li>Frank, Rupert L. and Siedentop, Heinz, el al. (2008) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-100456574">The Energy of Heavy Atoms According to Brown and Ravenhall: The Scott Correction</a>; <a href="https://doi.org/10.48550/arXiv.0805.4441">10.48550/arXiv.0805.4441</a></li>
<li>Frank, Rupert L. and Laptev, Ari (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-095723566">Spectral inequalities for Schrödinger operators with surface potentials</a>; <a href="https://doi.org/10.48550/arXiv.0711.3473">10.48550/arXiv.0711.3473</a></li>
<li>Ekholm, Tomas and Frank, Rupert L., el al. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170512-090412324">Remarks about Hardy inequalities on metric trees</a></li>
<li>Frank, Rupert L. and Loss, Michael, el al. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-073002205">Pόlya's conjecture in the presence of a constant magnetic field</a>; <a href="https://doi.org/10.48550/arXiv.0710.1078">10.48550/arXiv.0710.1078</a></li>
<li>Frank, Rupert L. and Hansson, Anders (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170510-090747676">Eigenvalue estimates for the Aharonov-Bohm operator in a domain</a>; <a href="https://doi.org/10.48550/arXiv.0710.1089">10.48550/arXiv.0710.1089</a></li>
<li>Benguria, Rafael D. and Frank, Rupert L., el al. (2007) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170511-064913855">The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space</a>; <a href="https://doi.org/10.48550/arXiv.0705.3833">10.48550/arXiv.0705.3833</a></li>
</ul>