Initial-irregular oblique derivative problems for nonlinear parabolic complex equations of second order with measurable coefficients

Abstract

This paper deals with initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic complex equations of second order in a multiply connected domain, where coefficients of equations are measurable. We first verify the uniqueness of solutions for the above problems, and then give a priori estimates of solutions for the problems. Finally, by using the above estimates and the Leray-Schauder theorem, the existence of solutions of the initial-boundary value problems is proved. The results in this paper are generalizations of corresponding theorems in [1],[4] and [5].