<h1>Frank, Rupert</h1>
<h2>Book Chapter from <a href="https://authors.library.caltech.edu">CaltechAUTHORS</a></h2>
<ul>
<li>Frank, Rupert L. (2024) <a href="https://authors.library.caltech.edu/records/dd468-e0p67">The Sharp Sobolev Inequality and Its Stability: An Introduction</a>; ISBN 978-3-031-67600-0; Geometric and Analytic Aspects of Functional Variational Principles; 1-64; <a href="https://doi.org/10.1007/978-3-031-67601-7_1">10.1007/978-3-031-67601-7_1</a></li>
<li>Frank, Rupert L. and Hainzl, Christian (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20200109-070444248">The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator</a>; ISBN 978-3-030-01601-2; Macroscopic Limits of Quantum Systems; 29-62; <a href="https://doi.org/10.1007/978-3-030-01602-9_2">10.1007/978-3-030-01602-9_2</a></li>
<li>Frank, Rupert L. and Nam, Phan Thành, el al. (2018) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20190513-100341402">A short proof of the ionization conjecture in Müller theory</a>; ISBN 978-1-4704-3681-0; Mathematical Problems in Quantum Physics; 1-12; <a href="https://doi.org/10.1090/conm/717/14437">10.1090/conm/717/14437</a></li>
<li>Frank, Rupert L. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-155923176">Eigenvalues of Schrödinger operators with complex surface potentials</a>; ISBN 978-3-03719-175-0; Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume; 245-259; <a href="https://doi.org/10.4171/175">10.4171/175</a></li>
<li>Frank, Rupert L. (2017) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290">Eigenvalue bounds for the fractional Laplacian: A review</a>; ISBN 9783110571561; Recent Developments in Nonlocal Theory; 210-235; <a href="https://doi.org/10.1515/9783110571561-007">10.1515/9783110571561-007</a></li>
<li>Frank, Rupert L. and Hainzl, Christian, el al. (2013) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-083839909">Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction</a>; ISBN 978-3-0348-0531-5; Operator Methods in Mathematical Physics; 57-88; <a href="https://doi.org/10.1007/978-3-0348-0531-5_3">10.1007/978-3-0348-0531-5_3</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H. (2012) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-075729792">A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality</a>; ISBN 978-3-0348-0263-5; Spectral Theory, Function Spaces and Inequalities; 55-67; <a href="https://doi.org/10.1007/978-3-0348-0263-5_4">10.1007/978-3-0348-0263-5_4</a></li>
<li>Frank, Rupert L. and Laptev, Ari, el al. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170526-100635987">A sharp bound on eigenvalues of Schröedinger operators on the half-line with complex-valued potentials</a>; ISBN 9783764399948; Spectral Theory and Analysis; 39-44; <a href="https://doi.org/10.1007/978-3-7643-9994-8_3">10.1007/978-3-7643-9994-8_3</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H., el al. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-075001254">Binding, Stability, and Non-binding of Multi-polaron Systems</a>; ISBN 9789814350365; Mathematical Results in Quantum Physics; 21-32; <a href="https://doi.org/10.1142/9789814350365_0002">10.1142/9789814350365_0002</a></li>
<li>Frank, Rupert L. and Geisinger, Leander (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-080935483">Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain</a>; ISBN 9789814350365; Mathematical Results in Quantum Physics; 138-147; <a href="https://doi.org/10.1142/9789814350365_0012">10.1142/9789814350365_0012</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H. (2011) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170501-070506766">Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality</a>; ISBN 978-0-8218-4971-2; Concentration, Functional Inequalities and Isoperimetry; 89-102; <a href="https://doi.org/10.48550/arXiv.1003.5248">10.48550/arXiv.1003.5248</a></li>
<li>Frank, Rupert L. and Lieb, Elliott H., el al. (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170526-125941569">Equivalence of Sobolev inequalities and Lieb-Thirring inequalities</a>; ISBN 978-981-4304-62-7; XVIth International Congress on Mathematical Physics; 523-535; <a href="https://doi.org/10.1142/9789814304634_0045">10.1142/9789814304634_0045</a></li>
<li>Frank, Rupert L. and Seiringer, Robert (2010) <a href="https://resolver.caltech.edu/CaltechAUTHORS:20170526-131557265">Sharp Fractional Hardy Inequalities in Half-Spaces</a>; ISBN 978-1-4419-1340-1; Around the Research of Vladimir Maz'ya I; 161-167; <a href="https://doi.org/10.1007/978-1-4419-1341-8_6">10.1007/978-1-4419-1341-8_6</a></li>
</ul>