It is proved that a function can be estimated in the norm with a higher degree of summability if it satisfies some integral relations similar to the reverse Hölder inequalities (quasireverse Hölder inequalities). As an example, we apply this result to derive an a priori estimate of the Hölder norm for a solution of strongly nonlinear elliptic system.
Si prova che una funzione può essere stimata nella norma con un grado più alto di sommabilità se soddisfa alcune relazioni integrali simili alle disuguaglianze di Hölder inverse (disuguaglianze di Hölder quasi-inverse). Come esempio applichiamo questo risultato per desumere una stima a priori di una norma di Hölder per una soluzione di un sistema ellittico fortemente non lineare.
@article{RLIN_2003_9_14_2_91_0,
author = {Arina A. Arkhipova},
title = {Quasireverse H\"older inequalities and a priori estimates for strongly nonlinear systems},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {14},
year = {2003},
pages = {91-108},
zbl = {1225.35082},
mrnumber = {2053660},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_2003_9_14_2_91_0}
}
Arkhipova, Arina A. Quasireverse Hölder inequalities and a priori estimates for strongly nonlinear systems. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 14 (2003) pp. 91-108. http://gdmltest.u-ga.fr/item/RLIN_2003_9_14_2_91_0/
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