Journal of Convex Analysis 21 (2014), No. 3, 715--726
Copyright Heldermann Verlag 2014
Sufficient Conditions for an Existence of a Solution to a Differential Inclusion
Waldemar Pompe
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
pompe@mimuw.edu.pl
[Abstract-pdf]
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 $\det B=1$.
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