On measure differential inclusions in optimal control theory.

Brandi, Primo; Salvadori, Anna

Displaying similar documents to “On measure differential inclusions in optimal control theory.”

The Euler equation for a class of nonconvex problems.

Buttazzo, Giuseppe, Faina, Loris (1994)

Portugaliae Mathematica

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Optimization problems for set functions.

Dorosiewicz, Slawomir (2001)

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Lower semicontinuity of multiple $μ$ -quasiconvex integrals

Ilaria Fragalà (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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Lower semicontinuity results are obtained for multiple integrals of the kind $\int_{ℝ^{n}} f (x, \nabla_{μ} u) d μ$ , where $μ$ is a given positive measure on $ℝ^{n}$ , and the vector-valued function $u$ belongs to the Sobolev space $H_{μ}^{1, p} (ℝ^{n}, ℝ^{m})$ associated with $μ$ . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to $μ$ . More precisely, for fully general $μ$ , a notion of quasiconvexity for $f$ along the tangent bundle to $μ$ , turns out to be necessary...