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arXiv · 2404.07614

On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology

Erasmo Caponio·Antonio Masiello·Stefan Suhr
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Abstract

We consider a differential inclusion on a manifold, defined by a field of open half-spaces whose boundary in each tangent space is the kernel of a one-form. We make the assumption that the corank one distribution associated to the kernel is completely nonholonomic of step 2. We identify a subset of solutions of the differential inclusion, satisfying two endpoints and periodic boundary conditions, which are homotopy equivalent in the $W^{1,p}$-topology, for any $p\in [1,+\infty)$, to the based loop space and the free loop space respectively.

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Erasmo Caponio, Antonio Masiello, Stefan Suhr. 2024-04-11. On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology. https://doi.org/10.1051/cocv%2F2024094

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