Geodesic
Sufficient Conditions for an Existence of a Solution to a Differential Inclusion
Journal of convex analysis, Tome 21 (2014) no. 3, pp. 715-726
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We formulate geometric conditions induced by the compact set $K\subset\mathbb{R}^{m\times n}$, which imply existence of a Lipschitz solution $u$ to the differential inclusion $Du\in K$. The solutions are obtained using the convex integration method. We illustrate our result for the known example $K=SO(2)\cup SO(2)B$, where $B$ is a $2\times2$ diagonal matrix with $\det B=1$. 
@article{JCA_2014_21_3_JCA_2014_21_3_a6,
     author = {W. Pompe},
     title = {Sufficient {Conditions} for an {Existence} of a {Solution} to a {Differential} {Inclusion}},
     journal = {Journal of convex analysis},
     pages = {715--726},
     year = {2014},
     volume = {21},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a6/}
}
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W. Pompe. Sufficient Conditions for an Existence of a Solution to a Differential Inclusion. Journal of convex analysis, Tome 21 (2014) no. 3, pp. 715-726. http://geodesic.mathdoc.fr/item/JCA_2014_21_3_JCA_2014_21_3_a6/