Inequalities

Essential tool when applying analysis to problems of practical importance

Commentaries.- I. Inequalities Related to Statistical Mechanics and Condensed Matter.- I.1 Theory of Ferromagnetism and the Ordering of Electronic Energy Levels.- I.2 Ordering Energy Levels of Interacting Spin Systems.- I.3 Entropy Inequalities (with H. Araki).- I.4 A Fundamental Property of Quantum-Mechanical Entropy.- I.5 Proof of the Strong Subadditivity of Quantum-Mechanical Entropy.- I.6 Some Convexity and Subadditivity Properties of Entropy.- I.7 A Refinement of Simon's Correlation Inequality.- I.8 Two Theorems on the Hubbard Model.- I.9 Magnetic Properties of Some Itinerant-Electron Systems at T > 0.- II. Matrix Inequalities and Combinatorics.- II.1 Proofs of Some Conjectures on Permanents.- II.2 Concavity Properties and a Generating Function for Stirling Numbers.- II.3 Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture.- II.4 Some Operator Inequalities of the Schwarz Type.- II.5 Inequalities for Some Operator and Matrix Functions.- II.6 Positive Linear Maps Which Are Order Bounded on C* Subalgebras.- II. 7 Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration Inequalities.- II. 8 Sharp Uniform Convexity and Smoothness Inequalities for Trace Norms.- II.9 A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy.- III. Inequalities Related to the Stability of Matter.- III.1 Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities.- III.2 On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators.- III.3 The Number of Bound States of One-Body Schrödinger Operators and the Weyl Problem.- III.4 Improved Lower Bound on the Indirect Coulomb Energy.- III.5 Density Functionals for Coulomb Systems.- III.6 On Characteristic Exponents in Turbulence.- III.7 Baryon Mass Inequalities in Quark Models.- III.8 Kinetic Energy Bounds and Their Application to the Stability of Matter.- III.9 A Sharp Bound for an Eigenvalue Moment of the One-Dimensional Schrödinger Operator.- IV. Coherent States.- IV.1 The Classical Limit of Quantum Spin Systems.- IV.2 Proof of an Entropy Conjecture of Wehrl.- IV.3 Quantum Coherent Operators: A Generalization of Coherent States.- IV.4 Coherent States as a Tool for Obtaining Rigorous Bounds.- V. Brunn-Minkowski Inequality and Rearrangements.- V.1 A General Rearrangement Inequality for Multiple Integrals.- V.2 Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma.- V.3 Best Constants in Young's Inequality, Its Converse and Its Generalization to More than Three Functions.- V.4 On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions and with an Application to the Diffusion Equation.- V.5 Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation.- V.6 Symmetric Decreasing Rearrangement Can Be Discontinuous.- V.7 The (Non) Continuity of Symmetric Decreasing Rearrangement.- V.8 On the Case of Equality in the Brunn-Minkowski Inequality for Capacity.- VI. General Analysis.- VI.1 An Lp Bound for the Riesz and Bessel Potentials of Orthonormal Functions.- VI.2 A Relation Between Pointwise Convergence of Functions and Convergence of Functionals.- VI.3 Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities.- VI.4 On the Lowest Eigenvalue of the Laplacian for the Intersection of Two Domains.- VI.5 Minimum Action Solutions of Some Vector Field Equations.- VI.6 Sobolev Inequalities with Remainder Terms (with H. Brezis).- VI.7 Gaussian Kernels Have Only Gaussian Maximizers.- VI.8 Integral Bounds for Radar Ambiguity Functions and Wigner Distributions.- VII. Inequalities Related to Harmonic Maps.- VII.1 Estimations d'énergie pour des applications de R3 à valeurs dans S2.- VII.2 Singularities of Energy Minimizing Maps from the Ball to the Sphere.- VII.3 Co-area, Liquid Crystals, and Minimal Surfaces.- VII.4 Counting Singularities in Liquid Crystals (with F. Almgren).- VII.5 Symmetry of the Ginzburg-Landau Minimizer in a Disc.- Publications of Elliott H. Lieb.