Generalised functions of bounded deformation

Dal Maso, Gianni. "Generalised functions of bounded deformation." Journal of the European Mathematical Society 015.5 (2013): 1943-1997. <http://eudml.org/doc/277561>.

@article{DalMaso2013,
abstract = {We introduce the space $GBD$ of generalized functions of bounded deformation and study the structure properties of these functions: the rectiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for $GBD$, which leads to a compactness result for the space $GSBD$ of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.},
author = {Dal Maso, Gianni},
journal = {Journal of the European Mathematical Society},
keywords = {free discontinuity problems; special functions of bounded deformation; jump set; rectifiability; slicing; approximate differentiability; free discontinuity problems; special functions of bounded deformation; jump set; rectifiability; slicing; approximate differentiability},
language = {eng},
number = {5},
pages = {1943-1997},
publisher = {European Mathematical Society Publishing House},
title = {Generalised functions of bounded deformation},
url = {http://eudml.org/doc/277561},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Dal Maso, Gianni
TI - Generalised functions of bounded deformation
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 5
SP - 1943
EP - 1997
AB - We introduce the space $GBD$ of generalized functions of bounded deformation and study the structure properties of these functions: the rectiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for $GBD$, which leads to a compactness result for the space $GSBD$ of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.
LA - eng
KW - free discontinuity problems; special functions of bounded deformation; jump set; rectifiability; slicing; approximate differentiability; free discontinuity problems; special functions of bounded deformation; jump set; rectifiability; slicing; approximate differentiability
UR - http://eudml.org/doc/277561
ER -