Regular Oblique Derivative Problems in Sobolev Spaces

ThisRegular oblique derivative problem chapterOblique derivative problem isElliptic differential operator devoted to the study of the regular oblique derivative problem for a second order, uniformly elliptic differential operator withSecond order elliptic differential operator discontinuous coefficients in the framework of \(L^{p}\) Sobolev spaces. More precisely, we consider a second order, uniformly elliptic differential operator withVMO (vanishing mean oscillation)@VMO vanishing mean oscillation (VMO) coefficientsVanishing mean oscillation (VMO) and an oblique derivative boundary operator that is nowhere tangential to the boundary. We state global regularizing property of the oblique derivative problem in the framework of \(L^{p}\) Sobolev spaces (Theorem 16.1). Furthermore, we state an existence and uniqueness theorem for the oblique derivative problem in the framework of \(L^{p}\) Sobolev spaces (Theorem 16.2).