Accession Number : ADA298295

Title :   Smoothness of the Scalar Coefficients in the Representations of Isotropic Tensor-Valued Functions.

Descriptive Note : Final rept. Feb-Apr 95,

Corporate Author : ARMY RESEARCH LAB ABERDEEN PROVING GROUND MD

Personal Author(s) : Scheidler, Michael J.

PDF Url : ADA298295

Report Date : AUG 1995

Pagination or Media Count : 40

Abstract : For a three-dimensional space, an isotropic tensor-valued function omega of a symmetric tensor A has the representation omega(A) = alpha(A)I + beta(A)A + gamma(A)A2, in which the coefficients alpha, beta, and gamma are isotropic scalar-valued functions. It is known that these coefficients may fail to be as smooth as omega at those tensors A that do not have three distinct eigenvalues. Serrin (1959) and Man (1994) determined conditions on the smoothness of P that guarantee the existence of continuous coefficients. We give a different proof of their results and also determine conditions on P that guarantee the existence of continuously differentiable coefficients. (AN)

Descriptors :   *TENSORS, *DIFFERENTIAL TOPOLOGY, MATRICES(MATHEMATICS), EIGENVALUES, THREE DIMENSIONAL, COEFFICIENTS, FUNCTIONAL ANALYSIS, SCALAR FUNCTIONS, NONLINEAR ANALYSIS, ORTHOGONALITY, VARIATIONAL PRINCIPLES.

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE