We consider a parabolic system in divergence form with measurable coefficients in a nonsmooth bounded domain to obtain a global gradient estimate for the weak solution in the setting of Orlicz space which is a natural generalization of Lp space. The coefficients are assumed to be merely measurable in one spatial variable and have small bounded mean oscillation semi-norms in all the other variables. The boundary of the domain can be locally approximated by a hyperplane, a so-called δ-Reifenberg domain which is beyond the Lipschitz category.

Parabolic systems with measurable coefficients in Reifenberg domain

PALAGACHEV, Dian Kostadinov;
2013

Abstract

We consider a parabolic system in divergence form with measurable coefficients in a nonsmooth bounded domain to obtain a global gradient estimate for the weak solution in the setting of Orlicz space which is a natural generalization of Lp space. The coefficients are assumed to be merely measurable in one spatial variable and have small bounded mean oscillation semi-norms in all the other variables. The boundary of the domain can be locally approximated by a hyperplane, a so-called δ-Reifenberg domain which is beyond the Lipschitz category.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11589/9874
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