Continuous Dependence on Modeling in the Cauchy Problem for Nonlinear Elliptic Equations

摘要

The Cauchy problem for various types of secondary order nonlinear elliptic equations is considered. A substitution v=epsilon u in the equation leads to a perturbed equation whose solution is compared to an appropriate solution of an unperturbed second order linear elliptic equation obtained by formally setting epsilon=O. In each case a logarithmic convexity argument is used to show that appropriately constrained solutions of the original equation (assumed to exist) are shown to differ from a solution of the associated linear equation in the manner depending continuously on the parameter epsilon.