1. IMPLICATIONS OF HADAMARD'S CONDITIONS FOR ELASTIC STABILITY WITH RESPECT TO UNIQUENESS THEOREMS
- Author
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J. L. Ericksen, R. A. Toupin, and Cardillo, Christian
- Subjects
General Mathematics ,010102 general mathematics ,Mathematical analysis ,Stability (learning theory) ,Type (model theory) ,[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph] ,01 natural sciences ,Displacement (vector) ,Stress (mechanics) ,Uniqueness theorem for Poisson's equation ,Hadamard transform ,0103 physical sciences ,010307 mathematical physics ,Boundary value problem ,Uniqueness ,0101 mathematics ,[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph] ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
Introduction. The purpose of this paper is to discuss implications of Hadamard's condition for elastic stability (2, §269) with respect to uniqueness of solutions of boundary value problems in the theory of small deformations superimposed on large. We show that a slightly refined form of his condition implies a uniqueness theorem for displacement boundary value problems. We construct a counter-example showing that his condition does not imply uniqueness of solutions for one type of stress boundary value problem.
- Published
- 1956