Functional Inequalities: New Perspectives and New Applications

By Nassif Ghoussoub, Amir Moradifam. 2012

169 citations recorded by the source corpus.

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 Hardy-Rellich type inequalities: Improved Hardy-Rellich inequalities on $H^2_0(\Omega)$ Weighted Hardy-Rellich inequalities on $H^2(\Omega)\cap H^1_0(\Omega)$ Critical dimensions for $4^{\textrm{th}}$ order nonlinear eigenvalue problems 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 Mass transport and optimal geometric inequalities: A general comparison principle for interacting gases Optimal Euclidean Sobolev inequalities Geometric inequalities Hardy-Rellich-Sobolev inequalities: The Hardy-Sobolev inequalities Domain curvature and best constants in the Hardy-Sobolev inequalities Aubin-Moser-Onofri inequalities: Log-Sobolev inequalities on the real line Trudinger-Moser-Onofri inequality on $\mathbb{S}^2$ Optimal Aubin-Moser-Onofri inequality on $\mathbb{S}^2$ Bibliography

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d04c2732e8892f0e936e6593a39fae50b4030dda

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Borderline Variational Problems Involving Fractional Laplacians and Critical Singularities (2015, background): “See for example [8], [9], [17], [19], [21] and [22].”
The sphere covering inequality and its applications (2016, background): “See Chapter 19 in [25] for a complete history of the problem.”
Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities (2015, background): “It is known (see, for instance, [24]) that HS(N, p, μ, s) is attained with the maximizers being the functions”
Factorizations and Hardy’s type identities and inequalities on upper half spaces (2019, methodology): “More precisely, we use the notion of Bessel pairs introduced by Ghoussoub and Moradifam [27,28] to establish several Hardy identities and inequalities with the general distance functions d(x) from x to a surface of any codimension.”