Geodesic
Hardy-Sobolev Inequalities for Hessian Integrals
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 951-967.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of $\log (|x|)$.
Usando appropriate tecniche di simmetrizzazione, si provano disuguaglianze di tipo Hardy-Sobolev per integrali Hessiani che estendono quelle classiche, ben note per le funzioni di Sobolev. Per tali disuguaglianze viene dato il valore della costante ottimale. Infine si stabilisce un miglioramento delle suddette disuguaglianze con l'aggiunta di un secondo termine che presenta un peso singolare dato da un'opportuna potenza negativa della funzione $\log (|x|)$. 
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     title = {Hardy-Sobolev {Inequalities} for {Hessian} {Integrals}},
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Gavitone, Nunzia. Hardy-Sobolev Inequalities for Hessian Integrals. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 951-967. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a34/

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