On a Normal Form for Second Order Elliptic Equations and Constructive Methods for Dirichlet's Problem.

摘要

In this work we consider quasilinear, second order elliptic equations in Euclidean spaces of arbitrary dimension. These equations are of the general type that occurs in the nonlinear membrane theory of elastic shells. Our approach enables us to define a normalization for dimensions greater than two. Furthermore, we are able to establish an iterative scheme which converges geometrically to the solution of the prescribed boundary value problem. These results generalize to dimensions greater than two the researches of Soviet mathematician, Academician Ilya N. Vekua.