A differential inclusion : the case of an isotropic set

Croce, Gisella

doi:10.1051/cocv:2004035

Croce, Gisella

ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 122-138

Résumé

In this article we are interested in the following problem: to find a map $u : Ω \to ℝ^{2}$ that satisfies

\{\begin{matrix} D u \in E & a.e. in Ω \\ u (x) = ϕ (x) & x \in \partial Ω \end{matrix}

where

Ω

is an open set of

ℝ^{2}

and

E

is a compact isotropic set of

ℝ^{2 \times 2}

. We will show an existence theorem under suitable hypotheses on

ϕ

.

MR Zbl

DOI : 10.1051/cocv:2004035

Classification : 34A60, 35F30, 52A30
Keywords: rank one convex hull, polyconvex hull, differential inclusion, isotropic set

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     author = {Croce, Gisella},
     title = {A differential inclusion : the case of an isotropic set},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {122--138},
     year = {2005},
     publisher = {EDP Sciences},
     volume = {11},
     number = {1},
     doi = {10.1051/cocv:2004035},
     mrnumber = {2110617},
     zbl = {1092.34004},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2004035/}
}

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Croce, Gisella. A differential inclusion : the case of an isotropic set. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 122-138. doi: 10.1051/cocv:2004035

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