We consider a parabolic system in divergence form with measurable coefficients in a non-smooth bounded domain when the associated nonhomogeneous term belongs to a weighted Orlicz space. We generalize the Calder\'{o}n-Zygmund theorem for the weak solution of such a system as an optimal estimate in weighted Orlicz spaces, by essentially proving that the spatial gradient is as integrable as the nonhomogeneous term under a possibly optimal assumption on the coefficients and a minimal geometric assumption on the boundary of the domain.
Parabolic systems with measurable coefficients in weighted Orlicz spaces
SOFTOVA PALAGACHEVA, Lyoubomira
2015
Abstract
We consider a parabolic system in divergence form with measurable coefficients in a non-smooth bounded domain when the associated nonhomogeneous term belongs to a weighted Orlicz space. We generalize the Calder\'{o}n-Zygmund theorem for the weak solution of such a system as an optimal estimate in weighted Orlicz spaces, by essentially proving that the spatial gradient is as integrable as the nonhomogeneous term under a possibly optimal assumption on the coefficients and a minimal geometric assumption on the boundary of the domain.File in questo prodotto:
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