Nonlinear Elliptic Equations with Small BMO Coefficients in Nonsmooth Domains in Generalized Morrey Spaces

We obtain the generalized Sobolev-Morrey spaces W1p,ϕ(Ω) estimate for weak solutions of a boundary value problem for nonlinear elliptic equations with BMO coefficients in nonsmooth domains. We investigate regularity of the weak solutions in generalized Morrey spaces Mp,ϕ(Ω). The nonlinearity has sufficiently small BMO seminorm and the boundary of the domain is sufficiently flat. © Zagreb