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Functional Inequalities: New Perspectives and New Applications
About this Title
Nassif Ghoussoub, University of British Columbia, Vancouver, BC, Canada and Amir Moradifam, Columbia University, New York, NY
Publication: Mathematical Surveys and Monographs
Publication Year:
2013; Volume 187
ISBNs: 978-0-8218-9152-0 (print); 978-1-4704-0947-0 (online)
DOI: https://doi.org/10.1090/surv/187
MathSciNet review: 3052352
MSC: Primary 35-02; Secondary 26Dxx, 35A23, 35J20, 35J60, 41A44, 42Bxx, 46E35
Table of Contents
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Front/Back Matter
Hardy type inequalities
- 1. Bessel pairs and Sturm’s oscillation theory
- 2. The classical Hardy inequality and its improvements
- 3. Improved Hardy inequality with boundary singularity
- 4. Weighted Hardy inequalities
- 5. The Hardy inequality and second order nonlinear eigenvalue problems
Hardy-Rellich type inequalities
- 6. Improved Hardy-Rellich inequalities on $H^2_0(\Omega )$
- 7. Weighted Hardy-Rellich inequalities on $H^2(\Omega )\cap H^1_0(\Omega )$
- 8. Critical dimensions for $4^{\textrm {th}}$ order nonlinear eigenvalue problems
Hardy inequalities for general elliptic operators
- 9. General Hardy inequalities
- 10. Improved Hardy inequalities for general elliptic operators
- 11. Regularity and stability of solutions in non-self-adjoint problems
Mass transport and optimal geometric inequalities
- 12. A general comparison principle for interacting gases
- 13. Optimal Euclidean Sobolev inequalities
- 14. Geometric inequalities
Hardy-Rellich-Sobolev inequalities
- 15. The Hardy-Sobolev inequalities
- 16. Domain curvature and best constants in the Hardy-Sobolev inequalities
Aubin-Moser-Onofri inequalities