Boundary regularity of unbounded weak solutions of the oblique derivative problem for a class of strongly nonlinear elliptic systems

The paper is devoted to a model setting of the oblique derivative problem for a class of quasilinear elliptic systems with strong nonlinearities in the gradient. Under a one-side condition for nonlinear terms, local regularity near the boundary for weak possibly unbounded solutions is studied. Earlier, the author studied local regularity of solutions for similar systems inside a given domain. The result of this paper is new even for description of the regular points inside a domain.