Advances in Differential Equations

Young measures, relaxation of functionals and existence results without weak lower semicontinuity

Gilles Aubert and Rabah Tahraoui

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Abstract

In this paper, we give new optimality conditions in terms of Young measures for nonconvex minimization problems of type Inf${\int _\Omega} f \bigl(x, u(x), Du(x) \bigr)\,dx$. The analysis of these conditions allows us to find sufficient assumptions for the existence of a minimum.

Article information

Source
Adv. Differential Equations, Volume 3, Number 2 (1998), 293-336.

Dates
First available in Project Euclid: 19 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366399900

Mathematical Reviews number (MathSciNet)
MR1750414

Zentralblatt MATH identifier
0949.49012

Subjects
Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 49J20: Optimal control problems involving partial differential equations 49Q20: Variational problems in a geometric measure-theoretic setting

Citation

Aubert, Gilles; Tahraoui, Rabah. Young measures, relaxation of functionals and existence results without weak lower semicontinuity. Adv. Differential Equations 3 (1998), no. 2, 293--336. https://projecteuclid.org/euclid.ade/1366399900


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