A posteriori error estimates for approximate solutions of variational problems with power growtn functionals

The present paper is concerned with the derivation of upper estimates of the difference $\|v-u\|$ where $u$ is a minimizer of a variational problem and $v$ is an element of the corresponding functional space. By using methods of duality theory, we derive a majorizing functional, which explicitly depends only on $v$ and the data of the problem. The advantage of this majorant is that it does not contain unknown constants and can be directly computed by simple numerical methods.