Calculus Of Variations

In this chapter, we study variational problems. In Sect. 7.1, we deal with calculus of variations problems. We prove lower semicontinuity results for integral functionals. This also leads to a brief presentation of the theory of Young measures. We also develop the Euler-Lagrange equation and discuss the Lavrentiev gap phenomenon. In Sect. 7.2, we deal with optimal control problems involving maximal monotone operators in their dynamics(unilateral constraints).