Published Paper
Inserted: 26 jul 2001
Last Updated: 13 nov 2002
Journal: ESAIM:COCV
Volume: 7
Pages: 495-519
Year: 2002
Abstract:
We study the integral representation properties of limits of sequences of integral functionals like \,$\int f(x,Du)\,dx$\, under nonstandard growth conditions of $(p,q)$-type: namely, we assume that $$ \vert z\vert{p(x)}\leq f(x,z)\leq L(1+\vert z\vert{p(x)})\,. $$ Under weak assumptions on the continuous function $\px$, we prove $\Gamma$-convergence to integral functionals of the same type. We also analyse the case of integrands $f(x,u,Du)$ depending explicitly on $u$; finally we weaken the assumption allowing $p(x)$ to be discontinuous on nice sets.
Keywords: Gamma-convergence, Integral representation, Nonstandard growth conditions
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