Discontinuous oblique derivative problems for second order quasi-linear mixed equations in general domains
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).
scientific article; zbMATH DE number 2082073