On Hardy inequalities with a remainder term

Details On Hardy inequalities with a remainder term On Hardy inequalities with a remainder term

2009-09-30

arxiv.org/abs/0909.5690v2

Mathematics

Analysis of PDEs

14 pages

Scientific paper

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. This result is new when the right hand side is a Lorentz norm of the gradient.

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