Caffarelli–Kohn–Nirenberg inequalities with remainder terms

Critical dimensions and higher order Sobolev inequalities with remainder terms ∗

Pucci and Serrin [21] conjecture that certain space dimensions behave “critically” in a semilinear polyharmonic eigenvalue problem. Up to now only a considerably weakened version of this conjecture could be shown. We prove that exactly in these dimensions an embedding inequality for higher order Sobolev spaces on bounded domains with an optimal embedding constant may be improved by adding a “li...

Hardy inequalities with optimal constants and remainder terms ∗

We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces W 1,p 0 and in higher-order Sobolev spaces on a bounded domain Ω ⊂ R can be refined by adding remainder terms which involve L norms. In the higher-order case further L norms with lower-order singular weights arise. The case 1 < p < 2 being more involved requires a different technique and is developed only...

On a Sobolev Inequality with Remainder Terms

In this note we consider the following Sobolev inequality

Caffarelli – Kohn – Nirenberg inequalities with remainder terms $ Zhi - Qiang Wanga and Michel

On Hardy inequalities with a remainder term

In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality a term which depends on some Lorentz norms of u or of its gradient and we find the best values of the constants for remaining terms. In both cases we show that the problem of finding the optimal value of the constant can be reduced to a spherically symmetric situation. Thi...