Edit Profile (opens in new tab) Frank, Rupert L. Compute Distance To: Compute 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 · Google Scholar · dblp Documents Indexed: 154 Publications since 2003, including 1 Book 3 Contributions as Editor Co-Authors: 84 Co-Authors with 139 Joint Publications 2,328 Co-Co-Authors all top 5 Co-Authors 18 single-authored 32 Lieb, Elliott Hershel 26 Seiringer, Robert 11 Laptev, Ari 8 Hainzl, Christian 7 König, Tobias 7 Lewin, Mathieu 6 Kovařík, Hynek 6 Phan Thành Nam 6 Sabin, Julien 5 Carlen, Eric Anders 5 Ekholm, Tomas 5 Larson, Simon 5 Siedentop, Heinz Karl Heinrich 5 Simon, Barry 5 Weidl, Timo 4 Geisinger, Leander 4 Loss, Michael 4 Pushnitski, Alexander B. 4 Solovej, Jan Philip 3 Merz, Konstantin 3 Thomas, Lawrence E. 3 Van Den Bosch, Hanne 2 Bellazzini, Jacopo 2 Benguria, Rafael D. 2 Carrillo de la Plata, José Antonio 2 Delgadino, Matias Gonzalo 2 Dolbeault, Jean 2 Exner, Pavel 2 Gontier, David 2 Ivanisvili, Paata 2 Lemm, Marius 2 Lenzmann, Enno 2 Safronov, Oleg 2 Schlein, Benjamin 2 Shterenberg, Roman G. 2 Tang, Hanli 2 Warzel, Simone 1 Behrndt, Jussi 1 Borichev, Aleksandr Aleksandrovich 1 Borrelli, William 1 Breuer, Jonathan 1 Chen, Shibing 1 Cornean, Horia D. 1 Dyda, Bartłomiej 1 Emmert, Lukas 1 Fournais, Søren 1 Gang, Zhou 1 Gesztesy, Fritz 1 González, María del Mar 1 Hansson, Anders M. 1 Helffer, Bernard 1 Hoffmann, Franca 1 Holden, Helge 1 Hundertmark, Dirk 1 Jeanjean, Louis 1 Jex, Michal 1 Jin, Tianling 1 Killip, Rowan 1 Kim, Seunghyeok 1 Kühn, Christian 1 Langmann, Edwin 1 Lenz, Daniel H. 1 Lotoreichik, Vladimir 1 Méhats, Florian 1 Molchanov, Stanislav Alekseevich 1 Monticelli, Dario Daniele 1 Morozov, Sergey 1 Naboko, Serguei N. 1 Olofsson, Rikard 1 Pistoia, Angela 1 Rohleder, Jonathan 1 Schimmer, Lukas 1 Silvestre, Luis E. 1 Sparber, Christof 1 Sukochev, Fedor Anatol’evich 1 Tan, Jinggang 1 Visciglia, Nicola 1 Volberg, Alexander Lvovich 1 Vugal’ter, Semën Abramovich 1 Weth, Tobias 1 Wingert, Daniel 1 Xiong, Jingang 1 Zanin, Dmitriy V. 1 Zhou, Gang all top 5 Serials 12 Communications in Mathematical Physics 8 Letters in Mathematical Physics 7 Journal of Functional Analysis 7 Calculus of Variations and Partial Differential Equations 7 Annales Henri Poincaré 6 Journal of Mathematical Physics 6 Advances in Mathematics 4 Journal of the European Mathematical Society (JEMS) 3 Communications on Pure and Applied Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Transactions of the American Mathematical Society 3 IMRN. International Mathematics Research Notices 3 SIAM Journal on Mathematical Analysis 3 Documenta Mathematica 3 Journal of Spectral Theory 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 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Analysis & PDE 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 St. Petersburg Mathematical Journal 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 Journal of Physics A: Mathematical and Theoretical 1 Bulletin of Mathematical Sciences 1 Séminaire Laurent Schwartz. EDP et Applications 1 Pure and Applied Functional Analysis 1 EMS Series of Congress Reports 1 Mathematics in Engineering 1 Pure and Applied Analysis 1 Probability and Mathematical Physics all top 5 Fields 90 Partial differential equations (35-XX) 64 Quantum theory (81-XX) 33 Operator theory (47-XX) 30 Functional analysis (46-XX) 25 Statistical mechanics, structure of matter (82-XX) 20 Real functions (26-XX) 15 Calculus of variations and optimal control; optimization (49-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Difference and functional equations (39-XX) 6 Potential theory (31-XX) 6 Information and communication theory, circuits (94-XX) 5 Probability theory and stochastic processes (60-XX) 4 Ordinary differential equations (34-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 138 Publications have been cited 2,446 times in 1,512 Documents Cited by ▼ Year ▼ Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis 208 2016 Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315Frank, Rupert L.; Lenzmann, Enno 206 2013 Nonlinear ground state representations and sharp Hardy inequalities. Zbl 1189.26031Frank, Rupert L.; Seiringer, Robert 173 2008 Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. Zbl 1202.35146Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 148 2008 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 83 2012 Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158Frank, Rupert L. 66 2011 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 65 2013 Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel 53 2014 Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1204.39024Frank, Rupert L.; Lieb, Elliott H. 53 2010 Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert 50 2006 Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola 48 2014 Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204Frank, Rupert L. 44 2018 Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018Frank, Rupert L.; Sabin, Julien 41 2017 The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three-dimensional upper half space. Zbl 1173.26011Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael 40 2008 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 39 2012 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061Frank, Rupert L.; Simon, Barry 36 2017 A compactness lemma and its application to the existence of minimizers for the liquid drop model. Zbl 1332.49042Frank, Rupert L.; Lieb, Elliott H. 32 2015 Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 32 2012 The critical temperature for the BCS equation at weak coupling. Zbl 1137.82025Frank, Rupert L.; Hainzl, Christian; Naboko, Serguei; Seiringer, Robert 31 2007 Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032Chen, Shibing; Frank, Rupert L.; Weth, Tobias 30 2013 On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074Frank, Rupert L.; Laptev, Ari; Safronov, Oleg 29 2016 On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Zbl 1106.81039Ekholm, T.; Frank, R. L. 29 2006 An extension problem for the CR fractional Laplacian. Zbl 1304.35747Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang 29 2015 Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163Frank, Rupert L.; Geisinger, Leander 28 2016 A simple proof of Hardy-Lieb-Thirring inequalities. Zbl 1184.35121Frank, Rupert L. 27 2009 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 25 2014 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 25 2014 Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025Dyda, Bartłomiej; Frank, Rupert L. 22 2012 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 21 2013 Sharp fractional Hardy inequalities in half-spaces. Zbl 1185.26044Frank, Rupert L.; Seiringer, Robert 21 2010 Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130Frank, Rupert L.; Zhou, Gang 21 2017 Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023Frank, Rupert L.; Loss, Michael 21 2012 Cwikel’s theorem and the CLR inequality. Zbl 1295.35347Frank, Rupert L. 21 2014 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150Frank, Rupert L.; König, Tobias 18 2019 Dynamics of a strongly coupled polaron. Zbl 1297.35202Frank, Rupert L.; Schlein, Benjamin 18 2014 Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069Frank, Rupert L.; Killip, Rowan; Phan Thành Nam 17 2016 The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 17 2018 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 16 2016 Singular spectrum for radial trees. Zbl 1177.05069Breuer, Jonathan; Frank, Rupert L. 16 2009 Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Zbl 1158.35021Frank, Rupert L.; Simon, Barry; Weidl, Timo 16 2008 A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086Frank, Rupert L.; Laptev, Ari; Seiringer, Robert 15 2011 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040Frank, Rupert; Lieb, Elliott H. 15 2018 Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061Frank, Rupert L.; Seiringer, Robert 15 2012 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 15 2011 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Zbl 1135.81030Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 14 2007 Pólya’s conjecture in the presence of a constant magnetic field. Zbl 1179.35205Frank, Rupert L.; Loss, Michael; Weidl, Timo 14 2009 Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. Zbl 1203.81072Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 13 2010 Some operator and trace function convexity theorems. Zbl 1342.47024Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 12 2016 Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303Frank, Rupert L. 12 2018 The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction. Zbl 1162.81037Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone 11 2008 The external field dependence of the BCS critical temperature. Zbl 1334.82080Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 11 2016 Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157Frank, Rupert L.; Simon, Barry 11 2011 Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026Frank, Rupert L.; Jin, Tianling; Xiong, Jingang 11 2018 Sharp decay estimates for critical Dirac equations. Zbl 1435.35053Borrelli, William; Frank, Rupert L. 11 2020 Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090Frank, Rupert L.; Geisinger, Leander 10 2012 A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128Frank, Rupert L.; Gang, Zhou 10 2020 On the asymptotic number of edge states for magnetic Schrödinger operators. Zbl 1131.35076Frank, Rupert L. 10 2007 Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031Frank, Rupert L.; Geisinger, Leander 9 2011 The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Zbl 1186.81137Frank, Rupert L.; Siedentop, Heinz; Warzel, Simone 9 2009 Binding of polarons and atoms at threshold. Zbl 1250.82046Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 9 2018 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022Frank, Rupert L.; Lieb, Elliott H. 9 2013 Eigenvalue estimates for Schrödinger operators on metric trees. Zbl 1237.35157Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 9 2011 The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne 7 2018 Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117Frank, Rupert L.; Lemm, Marius 7 2016 Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca 7 2019 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091Frank, Rupert L.; Lieb, Elliott H. 7 2017 Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486Frank, Rupert L.; Laptev, Ari 7 2008 Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016Frank, Rupert L.; Pushnitski, Alexander 7 2015 On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Zbl 1142.35374Frank, Rupert L. 6 2003 Number of bound states of Schrödinger operators with matrix-valued potentials. Zbl 1135.35052Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 6 2007 Remarks on eigenvalue estimates and semigroup domination. Zbl 1183.81068Frank, Rupert L. 6 2009 Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107Frank, Rupert L.; Larson, Simon 6 2020 Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan 6 2017 Absolute continuity of the spectrum for periodically modulated leaky wires in \({\mathbb{R}^{3}}\). Zbl 1206.82112Exner, Pavel; Frank, Rupert L. 6 2007 The spectral density of a product of spectral projections. Zbl 1312.81071Frank, Rupert L.; Pushnitski, Alexander 6 2015 Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. Zbl 1277.82073Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 6 2013 Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 6 2021 Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015Frank, Rupert L.; Schimmer, Lukas 5 2017 Lieb-Thirring inequalities on the half-line with critical exponent. Zbl 1147.35020Ekholm, Tomas; Frank, Rupert L. 5 2008 Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav 5 2008 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 1301.35070Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard 5 2013 Weakly coupled bound states of Pauli operators. Zbl 1205.35177Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon 5 2011 Existence and nonexistence in the liquid drop model. Zbl 1499.81093Frank, Rupert L.; Nam, Phan Thành 5 2021 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020Frank, Rupert L.; Lieb, Elliott H. 5 2021 Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. Zbl 1378.39013Frank, Rupert L.; Lieb, Elliott H. 5 2011 Entropy and the uncertainty principle. Zbl 1256.81022Frank, Rupert L.; Lieb, Elliott H. 4 2012 Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811Frank, Rupert L.; Pushnitski, Alexander 4 2019 Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354Frank, Rupert L.; Sabin, Julien 4 2018 Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015Frank, Rupert L.; Sabin, Julien 4 2017 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 4 2014 The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045Frank, Rupert L.; Geisinger, Leander 4 2015 Schrödinger operators: eigenvalues and Lieb-Thirring inequalities. Zbl 07595814Frank, Rupert L.; Laptev, Ari; Weidl, Timo 4 2023 Ground state properties of multi-polaron systems. Zbl 1304.82075Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 4 2014 Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161Frank, Rupert L.; Laptev, Ari 4 2010 Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela 4 2021 The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities. Zbl 1465.35015Frank, Rupert L.; Gontier, David; Lewin, Mathieu 4 2021 On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Zbl 1210.35040Frank, Rupert L.; Shterenberg, Roman G. 3 2004 On the spectrum of partially periodic operators. Zbl 1210.35041Frank, Rupert L.; Shterenberg, Roman G. 3 2007 The Stein-Tomas inequality in trace ideals. Zbl 1358.35010Frank, Rupert L.; Sabin, Julien 3 2016 Schrödinger operators: eigenvalues and Lieb-Thirring inequalities. Zbl 07595814Frank, Rupert L.; Laptev, Ari; Weidl, Timo 4 2023 Asymptotics of singular values for quantum derivatives. Zbl 07655327Frank, Rupert L.; Sukochev, Fedor; Zanin, Dmitriy 1 2023 Counting eigenvalues of Schrödinger operators with fast decaying complex potentials. Zbl 1498.35188Borichev, Alexander; Frank, Rupert L.; Volberg, Alexander 3 2022 Minimizers for a one-dimensional interaction energy. Zbl 1485.60006Frank, Rupert L. 2 2022 Which magnetic fields support a zero mode? Zbl 1498.81071Frank, Rupert L.; Loss, Michael 1 2022 An improved one-dimensional Hardy inequality. Zbl 07653497Frank, R. L.; Laptev, A.; Weidl, T. 1 2022 Equivalence of Sobolev norms involving generalized Hardy operators. Zbl 1470.81033Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz 6 2021 Existence and nonexistence in the liquid drop model. Zbl 1499.81093Frank, Rupert L.; Nam, Phan Thành 5 2021 Proof of spherical flocking based on quantitative rearrangement inequalities. Zbl 1478.49020Frank, Rupert L.; Lieb, Elliott H. 5 2021 Non-degeneracy for the critical Lane-Emden system. Zbl 1464.35097Frank, Rupert L.; Kim, Seunghyeok; Pistoia, Angela 4 2021 The nonlinear Schrödinger equation for orthonormal functions. II: Application to Lieb-Thirring inequalities. Zbl 1465.35015Frank, Rupert L.; Gontier, David; Lewin, Mathieu 4 2021 Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Zbl 1467.82092Frank, Rupert L.; Seiringer, Robert 3 2021 The Lieb-Thirring inequality revisited. Zbl 1467.35014Frank, Rupert L.; Hundertmark, Dirk; Jex, Michal; Nam, Phan Thành 3 2021 Hypercontractivity of the semigroup of the fractional Laplacian on the \(n\)-sphere. Zbl 1472.39048Frank, Rupert L.; Ivanisvili, Paata 2 2021 Inequalities for \(L^p\)-norms that sharpen the triangle inequality and complement Hanner’s inequality. Zbl 1475.46028Carlen, Eric A.; Frank, Rupert L.; Ivanisvili, Paata; Lieb, Elliott H. 2 2021 The periodic Lieb-Thirring inequality. Zbl 1480.81045Frank, Rupert L.; Gontier, David; Lewin, Mathieu 2 2021 The Lieb-Thirring inequalities: recent results and open problems. Zbl 07672908Frank, Rupert L. 2 2021 Energy asymptotics in the three-dimensional Brezis-Nirenberg problem. Zbl 07325918Frank, Rupert L.; König, Tobias; Kovařík, Hynek 1 2021 Sharp decay estimates for critical Dirac equations. Zbl 1435.35053Borrelli, William; Frank, Rupert L. 11 2020 A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. Zbl 1445.35128Frank, Rupert L.; Gang, Zhou 10 2020 Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Zbl 1467.35107Frank, Rupert L.; Larson, Simon 6 2020 On the error in the two-term Weyl formula for the Dirichlet Laplacian. Zbl 1458.35142Frank, Rupert L.; Larson, Simon 3 2020 Classification of solutions of an equation related to a conformal log Sobolev inequality. Zbl 1453.35036Frank, Rupert L.; König, Tobias; Tang, Hanli 3 2020 Proof of the strong Scott conjecture for Chandrasekhar atoms. Zbl 1465.81076Frank, Rupert L.; Merz, Konstantin; Siedentop, Heinz; Simon, Barry 2 2020 Inequalities that sharpen the triangle inequality for sums of \(N\) functions in \(L^p\). Zbl 1479.46029Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 1 2020 Liquid drop model for nuclear matter in the dilute limit. Zbl 1439.81090Emmert, Lukas; Frank, Rupert L.; König, Tobias 1 2020 Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent. Zbl 1421.35150Frank, Rupert L.; König, Tobias 18 2019 Reverse Hardy-Littlewood-Sobolev inequalities. Zbl 1442.35011Carrillo, José A.; Delgadino, Matías G.; Dolbeault, Jean; Frank, Rupert L.; Hoffmann, Franca 7 2019 Kato smoothness and functions of perturbed self-adjoint operators. Zbl 07078811Frank, Rupert L.; Pushnitski, Alexander 4 2019 Schatten class conditions for functions of Schrödinger operators. Zbl 07120692Frank, Rupert L.; Pushnitski, Alexander 3 2019 Periodic energy minimizers for a one-dimensional liquid drop model. Zbl 1428.82062Frank, Rupert L.; Lieb, Elliott H. 2 2019 Non-spherical equilibrium shapes in the liquid drop model. Zbl 1416.81223Frank, Rupert L. 2 2019 Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Zbl 1454.35102Frank, Rupert L.; König, Tobias 2 2019 The BCS critical temperature in a weak homogeneous magnetic field. Zbl 1427.82059Frank, Rupert L.; Hainzl, Christian; Langmann, Edwin 1 2019 Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains. Zbl 1421.35233Frank, R. L.; Laptev, A. 1 2019 Eigenvalue bounds for Schrödinger operators with complex potentials. III. Zbl 1390.35204Frank, Rupert L. 44 2018 The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Zbl 1386.49063Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 17 2018 A “liquid-solid” phase transition in a simple model for swarming, based on the “no flat-spots” theorem for subharmonic functions. Zbl 1420.49040Frank, Rupert; Lieb, Elliott H. 15 2018 Eigenvalue bounds for the fractional Laplacian: a review. Zbl 1404.35303Frank, Rupert L. 12 2018 Minimizers for the fractional Sobolev inequality on domains. Zbl 1393.26026Frank, Rupert L.; Jin, Tianling; Xiong, Jingang 11 2018 Inequalities for quantum divergences and the Audenaert-Datta conjecture. Zbl 1414.81064Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 9 2018 The maximal excess charge in Müller density-matrix-functional theory. Zbl 1397.81456Frank, Rupert L.; Phan Thành Nam; van den Bosch, Hanne 7 2018 Extremizers for the Airy-Strichartz inequality. Zbl 1406.35354Frank, Rupert L.; Sabin, Julien 4 2018 A short proof of the ionization conjecture in Müller theory. Zbl 1423.81198Frank, Rupert L.; Phan Thành Nam; Van Den Bosch, Hanne 2 2018 Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Zbl 1388.42018Frank, Rupert L.; Sabin, Julien 41 2017 Eigenvalue bounds for Schrödinger operators with complex potentials II. Zbl 1386.35061Frank, Rupert L.; Simon, Barry 36 2017 Derivation of an effective evolution equation for a strongly coupled polaron. Zbl 1365.35130Frank, Rupert L.; Zhou, Gang 21 2017 Norms of quantum Gaussian multi-mode channels. Zbl 1366.81091Frank, Rupert L.; Lieb, Elliott H. 7 2017 Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\). Zbl 1378.81026Behrndt, Jussi; Frank, Rupert L.; Kühn, Christian; Lotoreichik, Vladimir; Rohleder, Jonathan 6 2017 Endpoint resolvent estimates for compact Riemannian manifolds. Zbl 1360.58015Frank, Rupert L.; Schimmer, Lukas 5 2017 Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Zbl 1373.58015Frank, Rupert L.; Sabin, Julien 4 2017 Eigenvalues of Schrödinger operators with complex surface potentials. Zbl 1372.81057Frank, Rupert L. 2 2017 Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Zbl 1387.35549Frank, Rupert L.; Méhats, Florian; Sparber, Christof 2 2017 Uniqueness of radial solutions for the fractional Laplacian. Zbl 1365.35206Frank, Rupert L.; Lenzmann, Enno; Silvestre, Luis 208 2016 On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074Frank, Rupert L.; Laptev, Ari; Safronov, Oleg 29 2016 Refined semiclassical asymptotics for fractional powers of the Laplace operator. Zbl 1337.35163Frank, Rupert L.; Geisinger, Leander 28 2016 Nonexistence of large nuclei in the liquid drop model. Zbl 1347.49069Frank, Rupert L.; Killip, Rowan; Phan Thành Nam 17 2016 Maximizers for the Stein-Tomas inequality. Zbl 1357.42023Frank, Rupert L.; Lieb, Elliott H.; Sabin, Julien 16 2016 Some operator and trace function convexity theorems. Zbl 1342.47024Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 12 2016 The external field dependence of the BCS critical temperature. Zbl 1334.82080Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 11 2016 Multi-component Ginzburg-Landau theory: microscopic derivation and examples. Zbl 1351.82117Frank, Rupert L.; Lemm, Marius 7 2016 The Stein-Tomas inequality in trace ideals. Zbl 1358.35010Frank, Rupert L.; Sabin, Julien 3 2016 Incompatibility of time-dependent Bogoliubov-de-Gennes and Ginzburg-Landau equations. Zbl 1358.82041Frank, 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 1332.49042Frank, Rupert L.; Lieb, Elliott H. 32 2015 An extension problem for the CR fractional Laplacian. Zbl 1304.35747Frank, Rupert L.; del Mar González, María; Monticelli, Dario D.; Tan, Jinggang 29 2015 Trace class conditions for functions of Schrödinger operators. Zbl 1310.47016Frank, Rupert L.; Pushnitski, Alexander 7 2015 The spectral density of a product of spectral projections. Zbl 1312.81071Frank, Rupert L.; Pushnitski, Alexander 6 2015 The ground state energy of a polaron in a strong magnetic field. Zbl 1323.82045Frank, Rupert L.; Geisinger, Leander 4 2015 Weak perturbations of the \(p\)-Laplacian. Zbl 1322.49076Ekholm, Tomas; Frank, Rupert L.; Kovařík, Hynek 3 2015 Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. Zbl 1304.60081Frank, Rupert L.; Lenz, Daniel; Wingert, Daniel 53 2014 Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Zbl 1320.46026Bellazzini, Jacopo; Frank, Rupert L.; Visciglia, Nicola 48 2014 Stability estimates for the lowest eigenvalue of a Schrödinger operator. Zbl 1291.35145Carlen, Eric A.; Frank, Rupert L.; Lieb, Elliott H. 25 2014 Strichartz inequality for orthonormal functions. Zbl 1307.35245Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 25 2014 Cwikel’s theorem and the CLR inequality. Zbl 1295.35347Frank, Rupert L. 21 2014 Dynamics of a strongly coupled polaron. Zbl 1297.35202Frank, Rupert L.; Schlein, Benjamin 18 2014 Existence of ground states for negative ions at the binding threshold. Zbl 1302.81099Bellazzini, Jacopo; Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 4 2014 Ground state properties of multi-polaron systems. Zbl 1304.82075Frank, R. L.; Lieb, E. H.; Seiringer, R.; Thomas, L. E. 4 2014 Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\). Zbl 1307.35315Frank, Rupert L.; Lenzmann, Enno 206 2013 Monotonicity of a relative Rényi entropy. Zbl 1350.94020Frank, Rupert L.; Lieb, Elliott H. 65 2013 Remainder terms in the fractional Sobolev inequality. Zbl 1296.46032Chen, Shibing; Frank, Rupert L.; Weth, Tobias 30 2013 A positive density analogue of the Lieb-Thirring inequality. Zbl 1260.35088Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert 21 2013 Extended quantum conditional entropy and quantum uncertainty inequalities. Zbl 1280.81022Frank, Rupert L.; Lieb, Elliott H. 9 2013 Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. Zbl 1277.82073Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 6 2013 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 1301.35070Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard 5 2013 Symmetry of bipolaron bound states for small Coulomb repulsion. Zbl 1269.82064Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 3 2013 Heat kernels of metric trees and applications. Zbl 1278.47048Frank, Rupert L.; Kovařík, Hynek 3 2013 Sharp constants in several inequalities on the Heisenberg group. Zbl 1252.42023Frank, Rupert L.; Lieb, Elliott H. 83 2012 A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. Zbl 1297.39023Frank, Rupert L.; Lieb, Elliott H. 39 2012 Microscopic derivation of Ginzburg-Landau theory. Zbl 1251.35156Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip 32 2012 Fractional Hardy-Sobolev-Maz’ya inequality for domains. Zbl 1273.26025Dyda, Bartłomiej; Frank, Rupert L. 22 2012 Hardy-Sobolev-Maz’ya inequalities for arbitrary domains. Zbl 1233.49023Frank, Rupert L.; Loss, Michael 21 2012 Lieb-Thirring inequality for a model of particles with point interactions. Zbl 1278.81061Frank, Rupert L.; Seiringer, Robert 15 2012 Semi-classical analysis of the Laplace operator with Robin boundary conditions. Zbl 1253.35090Frank, Rupert L.; Geisinger, Leander 10 2012 Binding of polarons and atoms at threshold. Zbl 1250.82046Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert 9 2012 Entropy and the uncertainty principle. Zbl 1256.81022Frank, Rupert L.; Lieb, Elliott H. 4 2012 Eigenvalue bounds for Schrödinger operators with complex potentials. Zbl 1228.35158Frank, Rupert L. 66 2011 A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086Frank, Rupert L.; Laptev, Ari; Seiringer, Robert 15 2011 Stability and absence of binding for multi-polaron systems. Zbl 1227.82083Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. 15 2011 Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Zbl 1229.35157Frank, Rupert L.; Simon, Barry 11 2011 Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. Zbl 1253.47031Frank, Rupert L.; Geisinger, Leander 9 2011 ...and 38 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,520 Authors 86 Frank, Rupert L. 35 Seiringer, Robert 20 Lieb, Elliott Hershel 19 Wei, Juncheng 17 Lu, Guozhen 16 Hainzl, Christian 15 Laptev, Ari 14 Cuenin, Jean-Claude 14 Lewin, Mathieu 14 Phan Thành Nam 13 Abdellaoui, Boumediene 13 Squassina, Marco 12 Ambrosio, Vincenzo 12 Keller, Matthias 12 Simon, Barry 12 Solovej, Jan Philip 11 Kovařík, Hynek 11 Lam, Nguyen 11 Nguyễn Văn Hoàng 11 Peral Alonso, Ireneo 11 Suragan, Durvudkhan 10 Hong, Younghun 9 Esfahani, Amin 9 Fournais, Søren 9 González, María del Mar 9 Kachmar, Ayman 9 Lenz, Daniel H. 9 Lenzmann, Enno 9 Liu, Weiming 9 Niu, Miaomiao 9 Sabin, Julien 9 Sire, Yannick 9 Topaloglu, Ihsan 8 Berta, Mario 8 Christiansen, Jacob Stordal 8 Exner, Pavel 8 Hansmann, Marcel 8 Larson, Simon 8 Lotoreichik, Vladimir 8 Lundholm, Douglas 8 Miyagaki, Olimpio Hiroshi 8 Oliveira e Silva, Diogo 8 Ozawa, Tohru 8 Peng, Shuangjie 8 Rougerie, Nicolas 8 Ruzhansky, Michael V. 8 Siedentop, Heinz Karl Heinrich 8 Stefanov, Atanas G. 8 Tang, Zhongwei 8 Tomamichel, Marco 8 Valdinoci, Enrico 8 Yang, Jing 7 Ao, Weiwei 7 Bez, Neal 7 Chen, Lu 7 Choi, Woocheol 7 Cinti, Eleonora 7 Correggi, Michele 7 Hajaiej, Hichem 7 Hua, Bobo 7 Laugesen, Richard Snyder 7 Leopold, Nikolai 7 Mizutani, Haruya 7 Novaga, Matteo 7 Schlein, Benjamin 7 Wilde, Mark M. 7 Zinchenko, Maxim 6 Alves, Claudianor Oliveira 6 Bellazzini, Jacopo 6 Bhakta, Mousomi 6 Borrelli, William 6 Carrillo de la Plata, José Antonio 6 Dinh, Van Duong 6 Dipierro, Serena 6 Fall, Mouhamed Moustapha 6 Filippas, Stathis 6 Georgiev, Vladimir S. 6 Guo, Qing 6 Han, Yazhou 6 Huang, Xueping 6 Kassymov, Aidyn Adilovich 6 König, Tobias 6 Krejčiřík, David 6 Long, Wei 6 Loss, Michael 6 Musina, Roberta 6 Niu, Pengcheng 6 Primo, Ana R. M. 6 Psaradakis, Georgios 6 Rohleder, Jonathan 6 Schmidt, Marcel 6 Tao, Chunxia 6 Tertikas, Achilles 6 Weidl, Timo 6 Yang, Hui 6 Yang, Jianfu 6 Yang, Qiaohua 6 Zou, Wenming 5 Alama, Stan 5 An, Xiaoming ...and 1,420 more Authors all top 5 Cited in 246 Serials 89 Journal of Mathematical Physics 71 Journal of Functional Analysis 67 Calculus of Variations and Partial Differential Equations 60 Communications in Mathematical Physics 54 Nonlinear Analysis. Theory, Methods & Applications. 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