## Pointwise bounds for solutions of the Cauchy problem for elliptic equationsAn 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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approximating the solution arbitrary function auchy prob boundary value problems BOUNDS FOR SOLUTIONS bounds for w(P Bramble and Payne California 1 Attn Cauchy data Cauchy problem Cauchy surface choices choose coefficients computable constants convex function D. C. Attn denote derivatives Differential Differential equations differential equation defined Dirichlet integral DISTRIBUTION LIST Ml ELLIPTIC EQUATIONS elliptic operator applied elliptic partial differential EXTERNAL DISTRIBUTION LIST geometry George George N gradient Green's function Green's identity hand side harmonic function integrals involving Laboratory Washington Laboratory White Oak Laplace operator linear Maryland method is based method is sed NAVAL ORDNANCE NOL technical report obtain bounds Ordnance Laboratory White partial differential equation Partial equations pointwise bounds PORBOR positive constants priori bound Project auchy Title report deals rtial Schwarz inequality second-order elliptic partial SECTION SOLUTIONS OF THC surface integrals technical report 62-91 technique for approximating Unclassified This report University val Ordnance Laboratory Washington 25