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.

*"synopsis" may belong to another edition of this title.*

Nassif Ghoussoub, University of British Columbia, Vancouver, BC, Canada Amir Moradifam, Columbia University, New York, NY, USA

*"About this title" may belong to another edition of this title.*

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Quantity Available: 1

Seller

Rating

**Book Description **Book Condition: New. Depending on your location, this item may ship from the US or UK. Bookseller Inventory # 97808218915200000000

More Information About This Seller | Ask Bookseller a Question

Published by
American Mathematical Society, United States
(2013)

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Quantity Available: 1

Seller

Rating

**Book Description **American Mathematical Society, United States, 2013. Microfilm. Book Condition: New. 259 x 183 mm. Language: English . Brand New Book. 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 Holder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations. Bookseller Inventory # AAN9780821891520

More Information About This Seller | Ask Bookseller a Question

Published by
American Mathematical Society

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Quantity Available: 1

Seller

Rating

**Book Description **American Mathematical Society. Microfilm. Book Condition: new. BRAND NEW, Functional Inequalities: New Perspectives and New Applications, Nassif Ghoussoub, Amir Moradifam, 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 Holder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations. Bookseller Inventory # B9780821891520

More Information About This Seller | Ask Bookseller a Question

Published by
American Mathematical Society, United States
(2013)

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Quantity Available: 1

Seller

Rating

**Book Description **American Mathematical Society, United States, 2013. Microfilm. Book Condition: New. 259 x 183 mm. Language: English . Brand New Book. 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 Holder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations. Bookseller Inventory # AAN9780821891520

More Information About This Seller | Ask Bookseller a Question

Published by
American Mathematical Society
(2013)

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Quantity Available: 1

Seller

Rating

**Book Description **American Mathematical Society, 2013. UNK. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # CE-9780821891520

More Information About This Seller | Ask Bookseller a Question

Published by
American Mathematical Society
(2013)

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Hardcover
Quantity Available: 1

Seller

Rating

**Book Description **American Mathematical Society, 2013. Hardcover. Book Condition: New. book. Bookseller Inventory # 0821891529

More Information About This Seller | Ask Bookseller a Question

Published by
Amer Mathematical Society
(2013)

ISBN 10: 0821891529
ISBN 13: 9780821891520

New
Hardcover
Quantity Available: 1

Seller

Rating

**Book Description **Amer Mathematical Society, 2013. Hardcover. Book Condition: Brand New. 310 pages. 10.25x7.25x1.00 inches. In Stock. Bookseller Inventory # __0821891529

More Information About This Seller | Ask Bookseller a Question