Functional Inequalities: New Perspectives and New Applications: New Perspectives and New Applications

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American Mathematical Soc., Apr 9, 2013 - Mathematics - 299 pages
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
 

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Contents

Bessel Pairs and Sturms Oscillation Theory
3
The Classical Hardy Inequality and Its Improvements
19
Improved Hardy Inequality with Boundary Singularity
31
Weighted Hardy Inequalities
45
The Hardy Inequality and Second Order Nonlinear Eigenvalue
59
Improved HardyRellich Inequalities on H20 Ω
71
Weighted HardyRellich Inequalities on H2Ω H10 Ω
93
Critical Dimensions for 4th Order Nonlinear Eigenvalue Problems109 8 1 Fourth order nonlinear eigenvalue problems
109
Optimal Euclidean Sobolev Inequalities
181
Geometric Inequalities
191
The HardySobolev Inequalities
201
Domain Curvature and Best Constants in the HardySobolev
213
9
247
21
253
52
259
TrudingerMoserOnofri Inequality on S2
263

General Hardy Inequalities
125
Improved Hardy Inequalities For General Elliptic Operators
143
Regularity and Stability of Solutions in NonSelfAdjoint
157
A General Comparison Principle for Interacting Gases
171
Optimal AubinMoserOnofri Inequality on S2
275
Bibliography
289
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About the author (2013)

Nassif Ghoussoub, University of British Columbia, Vancouver, BC, Canada

Amir Moradifam, Columbia University, New York, NY, USA

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