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Continuous Dependence on Modeling in the Cauchy Problem for Nonlinear Elliptic Equations.
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA AIR WARFARE RESEARCH DEPT
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The Cauchy problem for various types of secondary order nonlinear elliptic equations is considered. A substitution vepsilon 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 epsilonO. 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.
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