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 / Byun, S. S.; Ok, J.; Palagachev, Dian Kostadinov; Softova, L. G.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 18:2(2016). [10.1142/S0219199715500182]

Parabolic systems with measurable coefficients in weighted Orlicz spaces

PALAGACHEV, Dian Kostadinov;
2016-01-01

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.
2016
Parabolic systems with measurable coefficients in weighted Orlicz spaces / Byun, S. S.; Ok, J.; Palagachev, Dian Kostadinov; Softova, L. G.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 18:2(2016). [10.1142/S0219199715500182]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/1692
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