On Hardy inequalities with a remainder term |
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Authors: | Angelo Alvino Roberta Volpicelli Bruno Volzone |
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Institution: | 1.Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”,Università degli Studi di Napoli “Federico II”,Naples,Italy;2.Dipartimento per le Tecnologie,Università degli Studi di Napoli “Parthenope”,Naples,Italy |
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Abstract: | In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality
a term that 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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