In many problems of interest the (Cauchy) surface traction is given as a function of position on the deformed surface. A class of loadings sufficiently general to include these problems is considered, and within the context of the traction problem in finite elasticity, a number of uniqueness results are established. This work extends results obtained for the mixed problem by Gurtin and Spector.
RESUM~
Dans plusieurs problerhes interessants la traction surfacique de Cauchy est donn6e comme une fonction de la position dans la surface deform6e, Une telle classe des charges, suffisamment g6fierale, est consider6e et un nombre des r6sultats d'unicit6 est 6tablit dans le cadre du problefiae de traction de l'elasticit6 non lin6aire. Cet ouure prolonge des r6sultats pour le probl~me mixte obtenus par Gurtin et Spector. * A natural configuration whose elasticity tensor is positive definite. * We use tensor as a synonym for linear transformation. ~ These operations will be with respect to the material point x. ~ Cf. Adams [3], p. 67. ยง Cf., e.g., Fichera [4], p. 384 and p. 279. * Cf., e.g., Adams [3], Lions and Magenes [5]. ~ We use smooth as a synonym for C 1. $ Cf. Spector [2, 6]. * Although the result is due to the author, this proof is due to Gurtin (private communication). See also Del Piero [7]. * The first is an obvious consequence of the arithmetic-geometric mean inequality. The second follows from the definition of the Hi-norm. * In fact, the two notions of stability are equivalent. ~ Cf. Equations (3.4) and (3.6).