Edit Profile (opens in new tab) Frank, Rupert L. Co-Author Distance Author ID: frank.rupert-l Published as: Frank, Rupert L.; Frank, R. L.; Frank, Rupert more...less Homepage: https://www.mathematik.uni-muenchen.de/~frank/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp Videos: carmin.tv Documents Indexed: 197 Publications since 2003, including 1 Book and 27 Additional arXiv Preprints 3 Contributions as Editor · 1 Further Contribution Co-Authors: 100 Co-Authors with 174 Joint Publications 2,952 Co-Co-Authors all top 5 Co-Authors 27 single-authored 37 Lieb, Elliott Hershel 29 Seiringer, Robert 14 Laptev, Ari 10 Larson, Simon 9 Lewin, Mathieu 8 Hainzl, Christian 8 König, Tobias 8 Kovařík, Hynek 8 Loss, Michael 7 Phan Thành Nam 6 Sabin, Julien 6 Siedentop, Heinz Karl Heinrich 5 Carlen, Eric Anders 5 Dolbeault, Jean 5 Ekholm, Tomas 5 Simon, Barry 5 Solovej, Jan Philip 5 Weidl, Timo 4 Geisinger, Leander 4 Lenzmann, Enno 4 Merz, Konstantin 4 Pushnitski, Alexander B. 4 Thomas, Lawrence E. 3 Gontier, David 3 Helffer, Bernard 3 Van Den Bosch, Hanne 2 Bellazzini, Jacopo 2 Benguria, Rafael D. 2 Carrillo de la Plata, José Antonio 2 Delgadino, Matias Gonzalo 2 Esteban, Maria J. 2 Exner, Pavel 2 Figalli, Alessio 2 Fournais, Søren 2 Hoffmann, Franca 2 Ivanisvili, Paata 2 Jin, Tianling 2 Lemm, Marius 2 Peteranderl, Jonas W. 2 Safronov, Oleg 2 Schlein, Benjamin 2 Shterenberg, Roman G. 2 Sukochev, Fedor Anatol’evich 2 Tang, Hanli 2 Warzel, Simone 2 Weth, Tobias 2 Zanin, Dmitriy V. 1 Behrndt, Jussi 1 Borichev, Aleksandr Aleksandrovich 1 Borrelli, William 1 Breuer, Jonathan 1 Chen, Shibing 1 Cianchi, Andrea 1 Cornean, Horia D. 1 Cuenin, Jean-Claude 1 Duong, Giao Ky 1 Dyda, Bartłomiej 1 Emmert, Lukas 1 Gang, Zhou 1 Gesztesy, Fritz 1 Goffeng, Magnus 1 González, María del Mar 1 Hansson, Anders M. 1 Hoffmann-Ostenhof, Thomas 1 Holden, Helge 1 Hundertmark, Dirk 1 Jeanjean, Louis 1 Jex, Michal 1 Kachmar, Ayman 1 Killip, Rowan 1 Kim, Seunghyeok 1 Kühn, Christian 1 Langmann, Edwin 1 Le, Thi Minh Thao 1 Lenz, Daniel H. 1 Lotoreichik, Vladimir 1 Matzke, Ryan W. 1 Maz’ya, Vladimir Gilelevich 1 Méhats, Florian 1 Mingione, Giuseppe 1 Molchanov, Stanislav Alekseevich 1 Monticelli, Dario Daniele 1 Morozov, Sergey 1 Naboko, Serguei N. 1 Nguyen Phuoc Tai 1 Nicola, Fabio 1 Olofsson, Rikard 1 Sundqvist, Mikael Persson 1 Pick, Luboš 1 Pistoia, Angela 1 Read, Larry 1 Rohleder, Jonathan 1 Savin, Ovidiu V. 1 Schimmer, Lukas 1 Silvestre, Luis E. 1 Sparber, Christof 1 Tan, Jinggang 1 Tilli, Paolo 1 Van Schaftingen, Jean 1 Visciglia, Nicola ...and 6 more Co-Authors all top 5 Serials 13 Communications in Mathematical Physics 8 Letters in Mathematical Physics 8 Journal of Functional Analysis 8 Calculus of Variations and Partial Differential Equations 7 Advances in Mathematics 7 Annales Henri Poincaré 6 Journal of Mathematical Physics 4 Transactions of the American Mathematical Society 4 Journal of the European Mathematical Society (JEMS) 4 Journal of Spectral Theory 3 Communications on Pure and Applied Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 IMRN. International Mathematics Research Notices 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 SIAM Journal on Mathematical Analysis 3 Documenta Mathematica 3 Analysis & PDE 3 Pure and Applied Functional Analysis 2 Arkiv för Matematik 2 Reviews in Mathematical Physics 2 Duke Mathematical Journal 2 Indiana University Mathematics Journal 2 Mathematische Annalen 2 Proceedings of the American Mathematical Society 2 Journal of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 St. Petersburg Mathematical Journal 1 Studia Mathematica 1 Acta Mathematica 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Journal of the London Mathematical Society. Second Series 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the London Mathematical Society. Third Series 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Asymptotic Analysis 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Linear Algebra and its Applications 1 Journal of Mathematical Sciences (New York) 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Advanced Nonlinear Studies 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications in Mathematical Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Cambridge Studies in Advanced Mathematics 1 Lecture Notes in Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Advances in Calculus of Variations 1 Bulletin of Mathematical Sciences 1 Séminaire Laurent Schwartz. EDP et Applications 1 EMS Series of Congress Reports 1 Mathematics in Engineering 1 Pure and Applied Analysis 1 Probability and Mathematical Physics all top 5 Fields 102 Partial differential equations (35-XX) 72 Quantum theory (81-XX) 39 Operator theory (47-XX) 35 Functional analysis (46-XX) 26 Statistical mechanics, structure of matter (82-XX) 24 Real functions (26-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 7 Difference and functional equations (39-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Potential theory (31-XX) 6 Information and communication theory, circuits (94-XX) 5 Ordinary differential equations (34-XX) 5 Probability theory and stochastic processes (60-XX) 4 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 160 Publications have been cited 3,566 times in 2,142 Documents Cited by ▼ Year ▼ Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206 Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis 299 2016 Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315 Frank, Rupert L.; Lenzmann, Enno 282 2013 Nonlinear ground state representations and sharp Hardy inequalities. Zbl 1189.26031 Frank, Rupert L.; Seiringer, Robert 250 2008 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 196 2008 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023 Frank, Rupert L.; Lieb, Elliott H. 119 2012 Monotonicity of a relative Rényi entropy. Zbl 1350.94020 Frank, Rupert L.; Lieb, Elliott H. 89 2013 Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158 Frank, Rupert L. 73 2011 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024 Frank, Rupert L.; Lieb, Elliott H. 70 2010 Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081 Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel 64 2014 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023 Frank, Rupert L.; Lieb, Elliott H. 63 2012 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382 Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 59 2006 Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026 Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola 59 2014 Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018 Frank, Rupert L.; Sabin, Julien 58 2017 Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204 Frank, Rupert L. 58 2018 The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three-dimensional upper half space. Zbl 1173.26011 Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael 54 2008 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061 Frank, Rupert L.; Simon, Barry 50 2017 Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032 Chen, Shibing; Frank, Rupert L.; Weth, Tobias 48 2013 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042 Frank, Rupert L.; Lieb, Elliott H. 47 2015 An extension problem for the CR fractional Laplacian. Zbl 1304.35747 Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang 41 2015 On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074 Frank, Rupert L.; Laptev, Ari; Safronov, Oleg 38 2016 On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Zbl 1106.81039 Ekholm, T.; Frank, R. L. 37 2006 The critical temperature for the BCS equation at weak coupling. Zbl 1137.82025 Frank, Rupert L.; Hainzl, Christian; Naboko, Serguei; Seiringer, Robert 37 2007 Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156 Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 36 2012 A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121 Frank, Rupert L. 35 2009 Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044 Frank, Rupert L.; Seiringer, Robert 34 2010 Strichartz inequality for orthonormal functions. Zbl 1307.35245 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 34 2014 Schrödinger operators: eigenvalues and Lieb-Thirring inequalities. Zbl 1536.35001 Frank, Rupert L.; Laptev, Ari; Weidl, Timo 34 2023 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 33 2014 Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163 Frank, Rupert L.; Geisinger, Leander 30 2016 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023 Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 29 2016 Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025 Dyda, Bartłomiej; Frank, Rupert L. 29 2012 Cwikel’s theorem and the CLR inequality. Zbl 1295.35347 Frank, Rupert L. 27 2014 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150 Frank, Rupert L.; König, Tobias 26 2019 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 25 2013 Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130 Frank, Rupert L.; Zhou, Gang 25 2017 Dynamics of a strongly coupled polaron. Zbl 1297.35202 Frank, Rupert L.; Schlein, Benjamin 24 2014 Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023 Frank, Rupert L.; Loss, Michael 24 2012 Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069 Frank, Rupert L.; Killip, Rowan; Phan Thành Nam 24 2016 The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063 Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 22 2018 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040 Frank, Rupert; Lieb, Elliott H. 22 2018 Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Zbl 1158.35021 Frank, Rupert L.; Simon, Barry; Weidl, Timo 21 2008 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 21 2007 Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303 Frank, Rupert L. 20 2018 Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205 Frank, Rupert L.; Loss, Michael; Weidl, Timo 19 2009 A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086 Frank, Rupert L.; Laptev, Ari; Seiringer, Robert 19 2011 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 19 2010 Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033 Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 18 2021 Singular spectrum for radial trees. Zbl 1177.05069 Breuer, Jonathan; Frank, Rupert L. 17 2009 Some operator and trace function convexity theorems. Zbl 1342.47024 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 17 2016 The Lieb-Thirring inequality revisited. Zbl 1467.35014 Frank, Rupert L.; Hundertmark, Dirk; Jex, Michal; Nam, Phan Thành 17 2021 Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092 Frank, Rupert L.; Seiringer, Robert 17 2021 Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097 Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela 17 2021 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 16 2018 Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036 Frank, Rupert L.; König, Tobias; Tang, Hanli 16 2020 Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026 Frank, Rupert L.; Jin, Tianling; Xiong, Jingang 16 2018 Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011 Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca 16 2019 Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031 Frank, Rupert L.; Geisinger, Leander 15 2011 Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157 Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 15 2011 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 15 2011 Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061 Frank, Rupert L.; Seiringer, Robert 15 2012 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020 Frank, Rupert L.; Lieb, Elliott H. 15 2021 The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction. Zbl 1162.81037 Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone 14 2008 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022 Frank, Rupert L.; Lieb, Elliott H. 14 2013 Sharp decay estimates for critical Dirac equations. Zbl 1435.35053 Borrelli, William; Frank, Rupert L. 13 2020 The external field dependence of the BCS critical temperature. Zbl 1334.82080 Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 13 2016 Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107 Frank, Rupert L.; Larson, Simon 13 2020 Existence and nonexistence in the liquid drop model. Zbl 1499.81093 Frank, Rupert L.; Nam, Phan Thành 13 2021 A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128 Frank, Rupert L.; Gang, Zhou 12 2020 Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090 Frank, Rupert L.; Geisinger, Leander 12 2012 Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157 Frank, Rupert L.; Simon, Barry 12 2011 The Lieb-Thirring inequalities: recent results and open problems. Zbl 1518.35002 Frank, Rupert L. 12 2021 On the asymptotic number of edge states for magnetic Schrödinger operators. Zbl 1131.35076 Frank, Rupert L. 12 2007 The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities. Zbl 1465.35015 Frank, Rupert L.; Gontier, David; Lewin, Mathieu 11 2021 The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Zbl 1186.81137 Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone 10 2009 Remarks on eigenvalue estimates and semigroup domination. Zbl 1183.81068 Frank, Rupert L. 10 2009 Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117 Frank, Rupert L.; Lemm, Marius 10 2016 Lieb-Thirring inequalities on the half-line with critical exponent. Zbl 1147.35020 Ekholm, Tomas; Frank, Rupert L. 9 2008 Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016 Frank, Rupert L.; Pushnitski, Alexander 9 2015 Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026 Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan 9 2017 Binding of polarons and atoms at threshold. Zbl 1250.82046 Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354 Frank, Rupert L.; Sabin, Julien 8 2018 Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161 Frank, Rupert L.; Laptev, Ari 8 2010 The Stein-Tomas inequality in trace ideals. Zbl 1358.35010 Frank, Rupert L.; Sabin, Julien 8 2016 Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486 Frank, Rupert L.; Laptev, Ari 8 2008 Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015 Frank, Rupert L.; Sabin, Julien 8 2017 On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Zbl 1142.35374 Frank, Rupert L. 7 2003 Liquid drop model for nuclear matter in the dilute limit. Zbl 1439.81090 Emmert, Lukas; Frank, Rupert L.; König, Tobias 7 2020 Entropy and the uncertainty principle. Zbl 1256.81022 Frank, Rupert L.; Lieb, Elliott H. 7 2012 Weakly coupled bound states of Pauli operators. Zbl 1205.35177 Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon 7 2011 An improved one-dimensional Hardy inequality. Zbl 1522.26015 Frank, R. L.; Laptev, A.; Weidl, T. 7 2022 Sharp trace asymptotics for a class of \(2D\)-magnetic operators. (Asymptotiques précisées pour la trace d’une classe d’opérateurs de Schrödinger magnétiques en dimension 2.) Zbl 1301.35070 Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard 7 2013 Heat kernels of metric trees and applications. Zbl 1278.47048 Frank, Rupert L.; Kovařík, Hynek 7 2013 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013 Frank, Rupert L.; Lieb, Elliott H. 7 2011 The BCS critical temperature in a weak homogeneous magnetic field. Zbl 1427.82059 Frank, Rupert L.; Hainzl, Christian; Langmann, Edwin 7 2019 The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456 Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne 7 2018 The spectral density of a product of spectral projections. Zbl 1312.81071 Frank, Rupert L.; Pushnitski, Alexander 7 2015 Proof of the strong Scott conjecture for Chandrasekhar atoms. Zbl 1465.81076 Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz; Simon, Barry 7 2020 Degenerate stability of some Sobolev inequalities. Zbl 1515.39016 Frank, Rupert L. 7 2022 Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015 Frank, Rupert L.; Schimmer, Lukas 7 2017 Logarithmic estimates for mean-field models in dimension two and the Schrödinger-Poisson system. Zbl 1489.35072 Dolbeault, Jean; Frank, Rupert L.; Jeanjean, Louis 7 2021 A characterization of \(\dot{W}^{1,p}(\mathbb{R}^d)\). Zbl 1548.46028 Frank, Rupert L. 2 2024 An inequality for the normal derivative of the Lane-Emden ground state. Zbl 1537.35266 Frank, Rupert L.; Larson, Simon 1 2024 Degenerate stability of the Caffarelli-Kohn-Nirenberg inequality along the Felli-Schneider curve. Zbl 1534.35117 Frank, Rupert L.; Peteranderl, Jonas W. 1 2024 Endpoint Schatten class properties of commutators. Zbl 1542.35266 Frank, Rupert L.; Sukochev, Fedor; Zanin, Dmitriy 1 2024 Blow-up of solutions of critical elliptic equations in three dimensions. Zbl 1546.35100 Frank, Rupert L.; König, Tobias; Kovařík, Hynek 1 2024 Hardy inequalities for large fermionic systems. Zbl 07902930 Frank, Rupert L.; Hoffmann-Ostenhof, Thomas; Laptev, Ari; Solovej, Jan Philip 1 2024 Schrödinger operators: eigenvalues and Lieb-Thirring inequalities. Zbl 1536.35001 Frank, Rupert L.; Laptev, Ari; Weidl, Timo 34 2023 Asymptotics of singular values for quantum derivatives. Zbl 1516.46046 Frank, Rupert L.; Sukochev, Fedor; Zanin, Dmitriy 6 2023 Sharp inequalities for coherent states and their optimizers. Zbl 1515.81154 Frank, Rupert L. 5 2023 The Scott conjecture for large Coulomb systems: a review. Zbl 1515.81228 Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 3 2023 Sharp Weyl laws with singular potentials. Zbl 1514.35300 Frank, Rupert L.; Sabin, Julien 3 2023 Lieb-Thirring inequalities and other functional inequalities for orthonormal systems. Zbl 07823084 Frank, Rupert L. 2 2023 Weyl’s law under minimal assumptions. Zbl 07936230 Frank, Rupert L. 2 2023 An improved one-dimensional Hardy inequality. Zbl 1522.26015 Frank, R. L.; Laptev, A.; Weidl, T. 7 2022 Degenerate stability of some Sobolev inequalities. Zbl 1515.39016 Frank, Rupert L. 7 2022 Minimizers for a one-dimensional interaction energy. Zbl 1485.60006 Frank, Rupert L. 6 2022 Reverse conformally invariant Sobolev inequalities on the sphere. Zbl 1484.46037 Frank, Rupert L.; König, Tobias; Tang, Hanli 4 2022 Counting eigenvalues of Schrödinger operators with fast decaying complex potentials. Zbl 1498.35188 Borichev, Alexander; Frank, Rupert L.; Volberg, Alexander 4 2022 Which magnetic fields support a zero mode? Zbl 1498.81071 Frank, Rupert L.; Loss, Michael 4 2022 Fast diffusion leads to partial mass concentration in Keller-Segel type stationary solutions. Zbl 1495.35108 Carrillo, J. A.; Delgadino, M. G.; Frank, R. L.; Lewin, M. 2 2022 On the spectrum of the Kronig-Penney model in a constant electric field. Zbl 1514.34144 Frank, Rupert L.; Larson, Simon 1 2022 The physics and mathematics of Elliott Lieb. The 90th anniversary. Volume I. Zbl 1491.46002 1 2022 Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033 Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 18 2021 The Lieb-Thirring inequality revisited. Zbl 1467.35014 Frank, Rupert L.; Hundertmark, Dirk; Jex, Michal; Nam, Phan Thành 17 2021 Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092 Frank, Rupert L.; Seiringer, Robert 17 2021 Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097 Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela 17 2021 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020 Frank, Rupert L.; Lieb, Elliott H. 15 2021 Existence and nonexistence in the liquid drop model. Zbl 1499.81093 Frank, Rupert L.; Nam, Phan Thành 13 2021 The Lieb-Thirring inequalities: recent results and open problems. Zbl 1518.35002 Frank, Rupert L. 12 2021 The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities. Zbl 1465.35015 Frank, Rupert L.; Gontier, David; Lewin, Mathieu 11 2021 Logarithmic estimates for mean-field models in dimension two and the Schrödinger-Poisson system. Zbl 1489.35072 Dolbeault, Jean; Frank, Rupert L.; Jeanjean, Louis 7 2021 Energy asymptotics in the three-dimensional Brezis-Nirenberg problem. Zbl 1511.35123 Frank, Rupert L.; König, Tobias; Kovařík, Hynek 6 2021 Hypercontractivity of the semigroup of the fractional Laplacian on the \(n\)-sphere. Zbl 1472.39048 Frank, Rupert L.; Ivanisvili, Paata 4 2021 The periodic Lieb-Thirring inequality. Zbl 1480.81045 Frank, Rupert L.; Gontier, David; Lewin, Mathieu 3 2021 Inequalities for \(L^p\)-norms that sharpen the triangle inequality and complement Hanner’s inequality. Zbl 1475.46028 Carlen, Eric A.; Frank, Rupert L.; Ivanisvili, Paata; Lieb, Elliott H. 3 2021 Partial differential equations, spectral theory, and mathematical physics. The Ari Laptev anniversary volume. Zbl 1465.35005 2 2021 Two consequences of Davies’ Hardy inequality. Zbl 1482.35019 Frank, R. L.; Larson, S. 2 2021 Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036 Frank, Rupert L.; König, Tobias; Tang, Hanli 16 2020 Sharp decay estimates for critical Dirac equations. Zbl 1435.35053 Borrelli, William; Frank, Rupert L. 13 2020 Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107 Frank, Rupert L.; Larson, Simon 13 2020 A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128 Frank, Rupert L.; Gang, Zhou 12 2020 Liquid drop model for nuclear matter in the dilute limit. Zbl 1439.81090 Emmert, Lukas; Frank, Rupert L.; König, Tobias 7 2020 Proof of the strong Scott conjecture for Chandrasekhar atoms. Zbl 1465.81076 Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz; Simon, Barry 7 2020 Energy asymptotics in the Brezis-Nirenberg problem: the higher-dimensional case. Zbl 1537.35031 Frank, Rupert L.; König, Tobias; Kovařík, Hynek 6 2020 On the error in the two-term Weyl formula for the Dirichlet Laplacian. Zbl 1458.35142 Frank, Rupert L.; Larson, Simon 3 2020 Inequalities that sharpen the triangle inequality for sums of \(N\) functions in \(L^p\). Zbl 1479.46029 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 2 2020 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150 Frank, Rupert L.; König, Tobias 26 2019 Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011 Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca 16 2019 The BCS critical temperature in a weak homogeneous magnetic field. Zbl 1427.82059 Frank, Rupert L.; Hainzl, Christian; Langmann, Edwin 7 2019 Non-spherical equilibrium shapes in the liquid drop model. Zbl 1416.81223 Frank, Rupert L. 6 2019 Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811 Frank, Rupert L.; Pushnitski, Alexander 5 2019 Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains. Zbl 1421.35233 Frank, R. L.; Laptev, A. 5 2019 Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062 Frank, Rupert L.; Lieb, Elliott H. 5 2019 Schatten class conditions for functions of Schrödinger operators. Zbl 07120692 Frank, Rupert L.; Pushnitski, Alexander 5 2019 Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Zbl 1454.35102 Frank, Rupert L.; König, Tobias 2 2019 Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204 Frank, Rupert L. 58 2018 The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063 Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 22 2018 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040 Frank, Rupert; Lieb, Elliott H. 22 2018 Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303 Frank, Rupert L. 20 2018 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 16 2018 Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026 Frank, Rupert L.; Jin, Tianling; Xiong, Jingang 16 2018 Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354 Frank, Rupert L.; Sabin, Julien 8 2018 The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456 Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne 7 2018 The BCS critical temperature in a weak external electric field via a linear two-body operator. Zbl 1414.82037 Frank, Rupert L.; Hainzl, Christian 2 2018 A short proof of the ionization conjecture in Müller theory. Zbl 1423.81198 Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 2 2018 Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018 Frank, Rupert L.; Sabin, Julien 58 2017 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061 Frank, Rupert L.; Simon, Barry 50 2017 Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130 Frank, Rupert L.; Zhou, Gang 25 2017 Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026 Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan 9 2017 Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015 Frank, Rupert L.; Sabin, Julien 8 2017 Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015 Frank, Rupert L.; Schimmer, Lukas 7 2017 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091 Frank, Rupert L.; Lieb, Elliott H. 7 2017 Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Zbl 1387.35549 Frank, Rupert L.; Méhats, Florian; Sparber, Christof 5 2017 Condensation of fermion pairs in a domain. Zbl 1372.82044 Frank, Rupert L.; Lemm, Marius; Simon, Barry 4 2017 Eigenvalues of Schrödinger operators with complex surface potentials. Zbl 1372.81057 Frank, Rupert L. 3 2017 Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206 Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis 299 2016 On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074 Frank, Rupert L.; Laptev, Ari; Safronov, Oleg 38 2016 Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163 Frank, Rupert L.; Geisinger, Leander 30 2016 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023 Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 29 2016 Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069 Frank, Rupert L.; Killip, Rowan; Phan Thành Nam 24 2016 Some operator and trace function convexity theorems. Zbl 1342.47024 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 17 2016 The external field dependence of the BCS critical temperature. Zbl 1334.82080 Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 13 2016 Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117 Frank, Rupert L.; Lemm, Marius 10 2016 The Stein-Tomas inequality in trace ideals. Zbl 1358.35010 Frank, Rupert L.; Sabin, Julien 8 2016 Incompatibility of time-dependent Bogoliubov-de-Gennes and Ginzburg-Landau equations. Zbl 1358.82041 Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert 3 2016 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042 Frank, Rupert L.; Lieb, Elliott H. 47 2015 An extension problem for the CR fractional Laplacian. Zbl 1304.35747 Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang 41 2015 Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016 Frank, Rupert L.; Pushnitski, Alexander 9 2015 The spectral density of a product of spectral projections. Zbl 1312.81071 Frank, Rupert L.; Pushnitski, Alexander 7 2015 The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045 Frank, Rupert L.; Geisinger, Leander 5 2015 Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076 Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 3 2015 Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081 Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel 64 2014 Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026 Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola 59 2014 Strichartz inequality for orthonormal functions. Zbl 1307.35245 Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 34 2014 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145 Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 33 2014 Cwikel’s theorem and the CLR inequality. Zbl 1295.35347 Frank, Rupert L. 27 2014 Dynamics of a strongly coupled polaron. Zbl 1297.35202 Frank, Rupert L.; Schlein, Benjamin 24 2014 Ground state properties of multi-polaron systems. Zbl 1304.82075 Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 5 2014 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099 Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 5 2014 Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315 Frank, Rupert L.; Lenzmann, Enno 282 2013 ...and 60 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,035 Authors 106 Frank, Rupert L. 46 Seiringer, Robert 25 Laptev, Ari 25 Wei, Juncheng 24 Lu, Guozhen 22 Lieb, Elliott Hershel 22 Ruzhansky, Michael V. 20 Hainzl, Christian 18 Keller, Matthias 17 Kovařík, Hynek 17 Lam, Nguyen 17 Phan Thành Nam 17 Squassina, Marco 17 Suragan, Durvudkhan 16 Abdellaoui, Boumediene 16 Cuenin, Jean-Claude 16 Guo, Yuxia 15 Lewin, Mathieu 15 Solovej, Jan Philip 14 Lotoreichik, Vladimir 14 Valdinoci, Enrico 13 Exner, Pavel 13 König, Tobias 13 Lenz, Daniel H. 13 Nguyễn Văn Hoàng 13 Oliveira e Silva, Diogo 13 Peng, Shaolong 12 Ambrosio, Vincenzo 12 Dipierro, Serena 12 Peng, Shuangjie 12 Peral Alonso, Ireneo 12 Simon, Barry 11 Kachmar, Ayman 11 Kassymov, Aidyn Adilovich 11 Krejčiřík, David 11 Novaga, Matteo 11 Su, Yu 11 Topaloglu, Ihsan 10 Berta, Mario 10 Brasco, Lorenzo 10 Chen, Lu 10 Correggi, Michele 10 Esfahani, Amin 10 Fournais, Søren 10 Guo, Yujin 10 Hong, Younghun 10 Larson, Simon 10 Lenzmann, Enno 10 Niu, Miaomiao 10 Schlein, Benjamin 10 Siedentop, Heinz Karl Heinrich 10 Sire, Yannick 10 Wilde, Mark M. 10 Yang, Qiaohua 9 Bhakta, Mousomi 9 Carrillo de la Plata, José Antonio 9 Dolbeault, Jean 9 Fanelli, Luca 9 Garofalo, Nicola 9 González, María del Mar 9 Guo, Qing 9 Hajaiej, Hichem 9 Korotyaev, Evgeny L. 9 Liu, Weiming 9 Merz, Konstantin 9 Miyagaki, Olimpio Hiroshi 9 Sabin, Julien 9 Stefanov, Atanas G. 9 Tang, Zhongwei 9 Tomamichel, Marco 9 Torres Ledesma, César Enrique 8 Alves, Claudianor Oliveira 8 Bellazzini, Jacopo 8 Bez, Neal 8 Christiansen, Jacob Stordal 8 Cinti, Eleonora 8 Do Ó, João M. 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