Differential inclusions for differential forms and applications to the calculus of variations

Ana Cristina Barroso, CMAF, Universidade de Lisboa

June 22, 2006

Abstract

In this talk we present some necessary and sufficient conditions for the existence of solutions in W_{0}^{1,∞}(Ω; Λ^{k}(ℝ^{n})) of differential inclusions of the type

dω ∈ E, a.e. in Ω

where E ⊆ Λ^{k+1}(ℝ^{n}) is a given set.

We will also show how these results can be applied to obtain existence of solutions for the non-convex variational problem

inf {∫_{Ω} f(dω(x)) dx : ω ∈ W_{0}^{1,∞}(Ω; Λ^{k}(ℝ^{n}))}.

This is joint work with S. Bandyopadhyay, B. Dacorogna and J. Matias.