## Differential and Integral Equations

### Young measures and relaxation of functionals for integrands $f(x,u(x),u'(x))$

#### Abstract

In this paper, we examine the question of optimality conditions in terms of Young's measures for a relaxed problem associated to a one-dimensional nonconvex problem of the calculus of variations of the type $\inf \int_a^b f(x,u(x),u' (x))dx.$ Once these conditions are established, we set sufficient conditions for the existence of solutions of the nonconvex problem.

#### Article information

Source
Differential Integral Equations, Volume 9, Number 1 (1996), 27-43.

Dates
First available in Project Euclid: 7 May 2013

Aubert, Gilles; Tahraoui, Rabah. Young measures and relaxation of functionals for integrands $f(x,u(x),u'(x))$. Differential Integral Equations 9 (1996), no. 1, 27--43. https://projecteuclid.org/euclid.die/1367969986