The energy function for a class of variational problems with vector-valued functions

Abstract

In this paper we consider the infinite-horizon variational problem with an integrand $f$ from a complete metric space of functions, introduced in Coleman, Marcus and Mizel [1] as a model for the determination of the thermodynamical equilibrium state of unidimensional bodies. We study the existence of extremals for this variational problems and continuity properties of the response function.