Non-Linear Initial Data for Second and Higher Order Semi-Linear Elliptic Equations.

摘要

Goursat problems occur when one investigates inclusion phenomena in elasticity, a problem of interest in aircraft design. We consider here almost linear, elliptic equations with generalized, non-linear, vector, data. A special case occurs in the case of non-linear Cauchy data for equations of 2n-order. Our iterative procedure allows us to directly solve this problem without first reducing the data to the linear form. The approach followed in this paper is function theoretic in spirit and provides a numerical scheme for calculating approximate solutions. (Author)