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On the existence of variations, possibly with pointwise gradient constraints

Simone Bertone; Arrigo Cellina — 2007

ESAIM: Control, Optimisation and Calculus of Variations

We propose a necessary and sufficient condition about the existence of variations, , of non trivial solutions $η \in W_{0}^{1, \infty} (Ω)$ to the differential inclusion $\nabla η (x) \in - \nabla u (x) + 𝐃$ .

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