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Item Details
| Title:
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FUNCTIONAL INEQUALITIES
NEW PERSPECTIVES AND NEW APPLICATIONS |
| By: |
Nassif Ghoussoub, Amir Moradifam |
| Format: |
Microfilm |
| List price:
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£113.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821891529 |
| ISBN 13: |
9780821891520 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 April, 2013 |
| Series: |
Mathematical Surveys and Monographs 187 |
| Pages: |
310 |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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