Functional inequalities : new perspectives and new applications /
"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approac...
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| 100 | 1 | |a Ghoussoub, N |q (Nassif), |d 1953- |0 http://viaf.org/viaf/109007011 | |
| 100 | 1 | |a Ghoussoub, N |q (Nassif), |d 1953- |1 http://viaf.org/viaf/109007011 | |
| 100 | 1 | |a Ghoussoub, N |q (Nassif), |d 1953- | |
| 245 | 1 | 0 | |a Functional inequalities : |b new perspectives and new applications / |c Nassif Ghoussoub, Amir Moradifam |
| 263 | |a 1304 | ||
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c 2013, ©2013 | |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c [2013] | |
| 264 | 4 | |c ©2013 | |
| 300 | |a pages cm | ||
| 300 | |a xxiv, 299 pages ; |c 26 cm | ||
| 336 | |a text |2 rdacontent | ||
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| 337 | |a unmediated |2 rdamedia | ||
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| 338 | |a volume |2 rdacarrier | ||
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| 490 | 1 | |a Mathematical surveys and monographs ; |v v. 187 | |
| 490 | 1 | |a Mathematical surveys and monographs ; |v volume 187 | |
| 490 | 1 | |a Mathematical surveys and monographs, |v volume 187 | |
| 500 | |a This WorldCat-derived record is shareable under Open Data Commons ODC-BY, with attribution to OCLC |5 CTY | ||
| 504 | |a Includes bibliographical references and index | ||
| 504 | |a Includes bibliographical references | ||
| 505 | 0 | 0 | |t 1. Bessel pairs and Sturm's oscillation theory |t 2. The classical Hardy inequality and its improvements |t 3. Improved Hardy inequality with boundary singularity |t 4. Weighted Hardy inequalities |t 5. The Hardy inequality and second order nonlinear eigenvalue problems |t 6. Improved Hardy-Rellich inequalities on $H^2_0(\Omega ) |a t7. Weighted Hardy-Rellich inequalities on $H^2(\Omega )\cap H^1_0(\Omega ) |a t8. Critical dimensions for $4^{\textrm {th}}$ order nonlinear eigenvalue problems |t 9. General Hardy inequalities |t 10. Improved Hardy inequalities for general elliptic operators |t 11. Regularity and stability of solutions in non-self-adjoint problems |t 12. A general comparison principle for interacting gases |t 13. Optimal Euclidean Sobolev inequalities |t 14. Geometric inequalities |t 15. The Hardy-Sobolev inequalities |t 16. Domain curvature and best constants in the Hardy-Sobolev inequalities |t 17. Log-Sobolev inequalities on the real line |t 18. Trudinger-Moser-Onofri inequality on $\mathbb {S}^2 |a t19. Optimal Aubin-Moser-Onofri inequality on $\mathbb {S}^2$ |
| 520 | |a "The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website | ||
| 530 | |a Also available in an electronic version | ||
| 650 | 0 | |a Harmonic analysis | |
| 650 | 0 | |a Inequalities (Mathematics) | |
| 650 | 7 | |a Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems |2 msc | |
| 650 | 7 | |a Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems |2 msc | |
| 650 | 7 | |a Functional analysis |x Linear function spaces and their duals |x Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems |2 msc | |
| 650 | 7 | |a Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory |2 msc | |
| 650 | 7 | |a Harmonic analysis on Euclidean spaces |x Harmonic analysis in several variables |x Maximal functions, Littlewood-Paley theory |2 msc | |
| 650 | 7 | |a Harmonic analysis |2 fast | |
| 650 | 7 | |a Inequalities (Mathematics) |2 fast | |
| 650 | 7 | |a Partial differential equations -- General topics -- Inequalities involving derivatives and differential and integral operators, inequalities for integrals |2 msc | |
| 650 | 7 | |a Partial differential equations -- General topics -- Variational methods |2 msc | |
| 650 | 7 | |a Partial differential equations |x General topics |x Inequalities involving derivatives and differential and integral operators, inequalities for integrals |2 msc | |
| 650 | 7 | |a Partial differential equations |x General topics |x Variational methods |2 msc | |
| 650 | 7 | |a Real functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators |2 msc | |
| 650 | 7 | |a Real functions |x Inequalities |x Inequalities involving derivatives and differential and integral operators |2 msc | |
| 700 | 1 | |a Moradifam, Amir, |d 1980- |0 http://viaf.org/viaf/296458003 | |
| 700 | 1 | |a Moradifam, Amir, |d 1980- |1 http://viaf.org/viaf/296458003 | |
| 700 | 1 | |a Moradifam, Amir, |d 1980- | |
| 776 | 1 | |w (OCoLC)898200149 | |
| 830 | 0 | |a Mathematical surveys and monographs ; |v no. 187 | |
| 830 | 0 | |a Mathematical surveys and monographs ; |v volume 187 | |
| 830 | 0 | |a Mathematical surveys and monographs |v no. 187 | |
| 880 | 0 | |6 505-00 |a Part 1. Hardy Type Inequalities. Bessel Pairs and Sturm's Oscillation Theory ; The Classical Hardy Inequality and Its Improvements ; Improved Hardy Inequality with Boundary Singularity ; Weighted Hardy Inequalities ; The Hardy Inequality and Second Order Nonlinear Eigenvalue Problems. -- Part 2. Hardy-Rellich Type Inequalities. Improved Hardy-Rellich Inequalities on H2 0 (Ω) ; Weighted Hardy-Rellich Inequalities on H2(Ω) H1 0 (Ω) ; Critical Dimensions for 4th Order Nonlinear Eigenvalue Problems. -- Part 3. Hardy Inequalities for General Elliptic Operators. General Hardy Inequalities ; Improved Hardy Inequalities For General Elliptic Operators ; Regularity and Stability of Solutions in Non-Self-Adjoint Problems. -- Part 4. Mass Transport and Optimal Geometric Inequalities. A General Comparison Principle for Interacting Gases ; Optimal Euclidean Sobolev Inequalities ; Geometric Inequalities. -- Part 5. Hardy-Rellich-Sobolev Inequalities. The Hardy-Sobolev Inequalities ; Domain Curvature and Best Constants in the Hardy-Sobolev Inequalities. -- Part 6. Aubin-Moser-Onofri Inequalities. Log-Sobolev Inequalities on the Real Line ; Trudinger-Moser-Onofri Inequality on S² ; Optimal Aubin-Moser-Onofri Inequality on S² | |
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