Abstract
We consider variational integral functionals ∫Ωg(x,u(x),Du(x))dx,where Ω is a bounded open subset in Rn and the integrand g(x,s,ξ)=f(x,ξ)+b(x)s is not subjected to any growth condition from above neither satisfies any regularity assumption, growing linearly with respect to the s-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 u∗ in order to obtain global and explicit estimates for the solutions of the following minimization problem min∫Ωg(x,u(x),Du(x))dx;u∈u∗+W01,1(Ω).
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