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.
|Autori interni:||PALAGACHEV, Dian Kostadinov|
|Titolo:||Parabolic systems with measurable coefficients in Reifenberg domain|
|Rivista:||INTERNATIONAL MATHEMATICS RESEARCH NOTICES|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1093/imrn/rns142|
|Appare nelle tipologie:||1.1 Articolo in rivista|