The oblique derivative problem for general second order quasilinear

Abstract

This paper deals with the oblique derivative boundary value problem for second order quasilinear equations of mixed elliptic-hyperbolic type. We first give the representation of solutions for this boundary value problem, afterwards prove uniqueness and existence of solutions of the problem, and then obtain apriori estimates of solutions. In books 1, 2 the author discussed the Dirichlet problem Tricomi problem for linear mixed equations of second order, e.g . Here we use a method different from those of other authors to prove unique solvability of solutions of the oblique derivative problem for quasilinear equations of mixed type; the results include corresponding results in [1], [2] as special cases.