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 ω. We make the assumption that the corank one distribution associated to the kernel of ω 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 W1,p-topology, for any p ∈ [1,+∞), to the based loop space and the free loop space respectively.
On homotopy properties of solutions of some differential inclusions in the W 1, P -topology / Caponio, E.; Masiello, A.; Suhr, S.. - In: ESAIM. COCV. - ISSN 1292-8119. - 31:(2025). [10.1051/cocv/2024094]
On homotopy properties of solutions of some differential inclusions in the W 1, P -topology
Caponio E.
;Masiello A.;Suhr S.
2025-01-01
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 ω. We make the assumption that the corank one distribution associated to the kernel of ω 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 W1,p-topology, for any p ∈ [1,+∞), to the based loop space and the free loop space respectively.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
