Journal of Elasticity

, Volume 123, Issue 2, pp 179–201 | Cite as

Stress Gradient Elasticity Theory: Existence and Uniqueness of Solution

  • Karam Sab
  • Frédéric Legoll
  • Samuel Forest


The objective of the present article is to assess the well-posedness of the stress gradient linear elastic problems recently introduced by Forest and Sab (Mech. Res. Commun. 40:16–25, 2012) and to formulate the corresponding existence and uniqueness theorems. In particular, we show that such theorems can be established in the case of the boundary value problems formulated in (Forest and Sab in Mech. Res. Commun. 40:16–25, 2012) with the corresponding boundary conditions.


Stress gradient elasticity Higher order elasticity Boundary conditions Existence and uniqueness of solution 

Mathematics Subject Classification (2000)

35D30 35J56 35Q74 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Laboratoire Navier (ENPC, IFSTTAR, CNRS UMR 8205)Université Paris-EstMarne-la-Vallée Cedex 2France
  2. 2.INRIA RocquencourtMATHERIALS project-teamLe Chesnay CedexFrance
  3. 3.MINES ParisTech, Centre des matériauxCNRS UMR 7633Evry CedexFrance

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