Abstract:

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above
problem is proved. In this article, the complex analytic method
is used, namely the corresponding problem for degenerate elliptic
complex equations of first order is firstly discussed, afterwards
the above problem for the degenerate elliptic equations of second
order is solved.

Key words: Boundary value problems, nonlinear elliptic equations, parabolic degeneracy