Parabolic Systems with Measurable Coefficients in Reifenberg Domains
Sun‐Sig Byun, Dian K. Palagachev, Lihe Wang · International Mathematics Research Notices · 2012
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.