Open AccessBook
Functional Inequalities: New Perspectives and New Applications
Nassif Ghoussoub,Amir Moradifam +1 more
- 31 Jan 2013
TL;DR: 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 inequalities and second order nonlinear eigenvalue problems Hardy-Rellich type inequalities.
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Abstract: 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
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Citations
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TL;DR: Sharp discrete Hardy–Rellich inequalities on graphs with optimal constants. New inequalities for .
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Potential Theory on Minimal Hypersurfaces II: Hardy Structures and Schrödinger Operators
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Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials
Gerassimos Barbatis,Konstantinos T. Gkikas,Achilles Tertikas +2 more
- 11 Jul 2022
TL;DR: In this paper , the authors studied various problems related to the Schrödinger operator Lμ = −∆− μd −2 K where dK denotes the distance to K and μ ≤ k/4.
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The Hardy-Schrödinger operator on the Poincaré Ball: compactness and multiplicity
Nassif Ghoussoub,Saikat Mazumdar,Frédéric Robert +2 more
- 01 Apr 2018
TL;DR: For the borderline Dirichlet problem, this article showed that there are infinitely many variational positive solutions provided that the domain has a positive hyperbolic mass and the mass is not vanishing.
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References
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
- 07 Jan 2013
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
TL;DR: The handbook of mathematical functions with formulas graphs and mathematical tables national bureau of standards applied mathematics series 55 that the authors provide for you will be ultimate to give preference.
•Book
Handbook of mathematical functions : with formulas, graphs, and mathematical tables
Milton Abramowitz,Irene A. Stegun +1 more
- 01 Jan 1970
18K
•Book
Ordinary differential equations
Philip Hartman
- 01 Jan 1964
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
9.4K
Handbook of Mathematical Functions with Formulas, Graphs,
Mathemalical Tables,Milton Abramowitz,Irene A. Stegun,A. G. Greenhill +3 more
- 01 Jan 1971
TL;DR: The DLMF as discussed by the authors is the successor to the NBS Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, published by the National Bureau of Standards.
5.7K