Discontinuous oblique derivative problems for second order quasi-linear mixed equations in general domains (Q1827001)

The oblique derivative boundary value problem for second-order linear and quasi-linear equations of mixed (elliptic-hyperbolic) type \[ u_{xx}+ \text{sgn\,}y\cdot u_{yy}= au_x+ bu_y+ cu+ d\tag{1} \] is considered for more general domain. Using the method of Wen's (deformations which transform the boundary curve of hyperbolic domain into the segment) the authors present solvability results for (1).