Differential and Integral Equations

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

Gilles Aubert and Rabah Tahraoui

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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

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

First available in Project Euclid: 7 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 49Q20: Variational problems in a geometric measure-theoretic setting


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

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