An Integral representation result for the Gamma-limit of functionals with non standard growth conditions in the case of elasticity

An integral representation result on regular functions is proved for the o -limit of a sequence of integral functionals defined in the vectorial case and modelled on elasticity theory functional Z z f (( x , e ( u )) dx where convex lagrangians satisfy a non-standard estimate $$ -c_{0} + c_{1} | \xi|^{alpha }leq f ( (x,\xi ) leq c_{0} + c_{2} | \xi|^{eta },quad 1 lt alpha leq eta lt rac {nalpha }{n-alpha },enskip c_{0}geq 0,enskip c_{1},c_{2} gt 0. $$ When the limit integrand does not show Lavrent'ev phenomenon the representation result is also true on the whole space W 1, f ( z ; R n ).