Pointwise estimates for oblique derivative problems in nonsmooth domains

There is a long history of studying boundary value problems for elliptic an d parabolic differential equations when the equation is posed ill a domain with sufficiently smooth boundary. In this paper. we prove some pointwise e stimates: and regularity results for solutions when a directional derivativ e is prescribed on the boundary, which satisfies an interior cone condition . we consider very weak hypotheses on the data of the problem. In particula r, we consider an optimal relation between the interior cent: and the direc tion of tile prescribed directional derivative. and we assume very little s moothness of the coefficients in the equation and the boundary condition. ( C) 2001 Academic Press.