Relaxation : are smooth functions still dense in Sobolev spaces under energy constraints?

par Paulin Huguet (IMT - Université de Toulouse)

lundi 22 juin 2026, 14:00 → 15:00 Europe/Paris

Salle Pellos (1R2-207)

In this presentation, we introduce the notion of relaxation for integral functionals in the one-dimensional case of the form $\int_O^L f(x,u(x),u'(x)) dx$, as well as the concept of Lavrentiev gap between two function spaces. We review two categories of results established in this field and present a new result for Lagrangians satisfying regularity assumptions only with respect to the state variable u(x). We then draw a sketch of its proof using a geometric approach. If time permits, we will conclude with a brief discussion of relaxation in the space BV.