Sobolev and Hardy–Littlewood–Sobolev inequalities
Copyright policy )Sobolev and Hardy–Littlewood–Sobolev inequalities
This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type inequalities. Then we focus our attention on the constants in our improved Sobolev inequalities, that can be estimated by completion of the square methods. Our estimates rely on nonlinear flows and spectral problems based on a linearization around optimal Aubin-Talenti functions.
- Paris Dauphine University France
Onofri's inequality, Hardy-Littlewood-Sobolev inequality, Sobolev inequality, fast diffusion equation, best constants, Inequalities involving derivatives and differential and integral operators, Analyse, 510, Caffarelli-Kohn-Nirenberg inequalities, logarithmic Hardy-Littlewood-Sobolev inequality, extremal functions, stereographic projection, Mathematics - Analysis of PDEs, 515, Sobolev spaces, FOS: Mathematics, Nonlinear parabolic equations, duality, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis of PDEs (math.AP)
Onofri's inequality, Hardy-Littlewood-Sobolev inequality, Sobolev inequality, fast diffusion equation, best constants, Inequalities involving derivatives and differential and integral operators, Analyse, 510, Caffarelli-Kohn-Nirenberg inequalities, logarithmic Hardy-Littlewood-Sobolev inequality, extremal functions, stereographic projection, Mathematics - Analysis of PDEs, 515, Sobolev spaces, FOS: Mathematics, Nonlinear parabolic equations, duality, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Analysis of PDEs (math.AP)
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