Discontinuous Irregular Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order

It is known that in mechanics and physics, many problems have discontinu- ous boundary conditions (see (1)-(4)). In this paper, the discontinuous irregular oblique derivative problem (i.e. the discontinuous Poincare boundary value prob- lem) for nonlinear elliptic equations of second order in multiply connected domains is discussed. We first prove the uniqueness of solutions for the above boundary value problem, and then give a priori estimates of its solutions. Moreover by the Leray-Schauder theorem and compactness principle, the existence of solutions of the above problem for the second order equations is proved.