Tools

LEADER 04498cam 2200505 i 4500

001 ocn823209440;

003 OCoLC;

005 20141212054221.0;

008 130225s2013 riu b 000 0 eng ;

010 a| 2012045837;

020 a| 9780821891520 (alk. paper);

020 a| 0821891529 (alk. paper);

029 1 a| AU@b| 000050593036;

035 a| (Sirsi) o823209440;

035 a| (OCoLC)823209440;

042 a| pcc;

049 a| EREE;

050 00 a| QA295b| .G485 2013;

066 c| (S;

082 00 a| 515/.3532| 23;

084 a| 42B25a| 35A23a| 26D10a| 35A15a| 46E352| msc;

100 1 a| Ghoussoub, N.q| (Nassif),d| 1953-=| ^A206026;

245 10 a| Functional inequalities :b| new perspectives and new applications /c| Nassif Ghoussoub, Amir Moradifam.;

264 1 a| Providence, Rhode Island :b| American Mathematical Society,c| [2013];

300 a| xxiv, 299 pages ;c| 26 cm.;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

490 1 a| Mathematical surveys and monographs ;v| v. 187;

504 a| Includes bibliographical references.;

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.;

650 0 a| Inequalities (Mathematics)=| ^A22093;

650 0 a| Harmonic analysis.=| ^A25604;

700 1 a| Moradifam, Amir,d| 1980-=| ^A1161341;

830 0 a| Mathematical surveys and monographsv| no. 187.=| ^A638333;

880 0 6| 505-00/(Sa| 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.;

949 a| QA295 .G485 2013h| JOYNER48o| jmpli| 30372016203652;

938 a| YBP Library Servicesb| YANKn| 9968760;

938 a| Blackwell Book Serviceb| BBUSn| 9968760;

994 a| C0b| ERE;

596 a| 1;

998 a| 3320195;

999 a| QA295 .G485 2013w| LCc| 1i| 30372016203652l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 7/30/2013x| BOOKz| JSTACKSo| .STAFF. jmpl;

Functional inequalities : new perspectives and new applications / Nassif Ghoussoub, Amir Moradifam.

Author/creator	Ghoussoub, N., 1953-
Other author	Moradifam, Amir, 1980-
Format	Book
Publication	Providence, Rhode Island : American Mathematical Society, [2013]
Copyright Date	©2013
Description	xxiv, 299 pages ; 26 cm.
Subjects	Inequalities (Mathematics) Harmonic analysis.

Series	Mathematical surveys and monographs ; v. 187 Mathematical surveys and monographs no. 187. ^A638333
Abstract	"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.
Bibliography note	Includes bibliographical references.
LCCN	2012045837
ISBN	9780821891520 (alk. paper)
ISBN	0821891529 (alk. paper)

Availability

Library	Location	Call Number	Status	Item Actions
Joyner	General Stacks	QA295 .G485 2013	✔ Available	Place Hold

Functional inequalities : new perspectives and new applications / Nassif Ghoussoub, Amir Moradifam.

Click here for more information about this title

Availability