On general boundary-value problems for nonlinear elliptic equations of second order in a multiply connected plane domain (Q1914896)

This paper deals with some general irregular oblique derivative problem for nonlinear uniformly elliptic equations of second order in a multiply connected plane domain. The authors state the well posedness of a new set of modified boundary conditions, and verify the existence of solutions of the modified boundary value problem for harmonic functions. They prove the solvability of the modified problem for nonlinear elliptic equations. Here, the location of the zeros of analytic functions, a priori estimates for solutions and the continuation method are used in deriving these results.