SOME BOUNDARY VALUE PROBLEMS FOR SECOND ORDER MIXED EQUATIONS WITH DEGENERATE LINES

摘要

In [1-4], the authors posed and discussed the Tricomi problem of second order equations of mixed type, and in [6], the author discussed the oblique derivative problems of second order equations of mixed type without parabolic degeneracy. The present paper deals with some discontinuous oblique derivative problems for second order linear equations of mixed (elliptic-hyperbolic) type with parabolic degeneracy. Firstly, we give the formulation and representation of solutions of the above boundary value problems, and then prove the existence of solutions for the problems, in which we use the complex analytic method, namely the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used (see [5,6]).