Pointwise bounds for minimizers of some anisotropic functionals

We consider variational integral functionals [Formula presented]where [Formula presented] is a bounded open subset in [Formula presented] and the integrand [Formula presented] is not subjected to any growth condition from above neither satisfies any regularity assumption, growing linearly with respect to the [Formula presented]-variable. Their interest relies on the fact that they are strictly connected with optimal transport problems with congestion effects. The aim of this paper is to find sufficient conditions on the boundary datum [Formula presented] in order to obtain global and explicit estimates for the solutions of the following minimization problem [Formula presented]