Pointwise Bounds For Solutions Of The Cauchy Problem For Elliptic Equations

Pointwise Bounds for Solutions of the Cauchy Problem for Elliptic Equations

An analysis is presented which deals with a technique for approximating the solution to a Cauchy problem for a geneal second-order elliptic patil differential equation defined in an N-dimensional region D. The method is based upon the determination of an a priori bound for the value of an arbitrary function u at a point P in D in terms of the values of u and its gradient on the cauchy surface andA FUNCTIONAL OF THE ELLIPTIC OPERATOR APPLIED TO U. (Author).

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Pointwise Bounds in the Cauchy Problem for Elliptic Systems of Partial Differential Equations

This report developes a technique for approximating the solution to a Cauchy problem for a class of second order elliptic partial differential equations in N independent variables. The method is based upon the determination of an a priori bound for an arbitrary u(alpha) at a point P in terms of the values of the u(alpha) and their gradients on the Cauchy surface, and of a functional of the elliptic operator applied to the u(alpha). (Author).