Nonlinear poincaré problem for a system of first-order elliptic equations in the plane

Abstract

This paper deals with boundary value problem for the first order qualilinear elliptic systems in the plane

where G is a unit disk with the boundary Г D is the Douglis' differential operator Taking account of different signs for the problem's index n, first some a-priori estimates for the linear problem are given, then existence and uniqueness of the classical solution to the nonlinear problem are established under some hypotheses and well-posed conditions by a combination of an imbedding method with a Newton method.

AMS (MOS):

• 30E25