Abstract

We formulate geometric conditions induced by the compact set K⊂Rm×nK\subset\mathcal{R}^{m\times n}, which imply existence of a Lipschitz solution uu to the differential inclusion Du∈KDu\in K. The solutions are obtained using the convex integration method. We illustrate our result for the known example K=SO(2)∪SO(2)BK=SO(2)\cup SO(2)B, where BB is a 2×22\times2 diagonal matrix with det⁡B=1\det B=1

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Waldemar Pompe

Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland

pompe@mimuw.edu.pl

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Suggested citation

W. Pompe. “Sufficient Conditions for an Existence of a Solution to a Differential Inclusion.” Journal of Convex Analysis 21 (2014), No. 3, 715–726. https://doi.org/10.68381/jca21038

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press LLC.