On the existence of variations, possibly with pointwise gradient constraints

We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions eta is an element of W-0(1,infinity) (Omega) to the differential inclusion del eta(x) is an element of -del u(x) + D.

We propose a necessary and sufficient condition about the existence of variations, i.e., of non trivial solutions eta; ∈ W₀^1,∞(Ω) to the differential inclusion ∇ _η(x) ∈ - ∇u(x) + D. © EDP Sciences, SMAI 2007.