On Lᵖ inequality for differential forms and Lᵖ cohomology of a semialgebraic set for p>>1

الأصل · EN

We study Poincaré type Lᵖ inequality on a compact semialgebraic subset of ⁿ for p>>1. First we derive a local inequality by using a Lipschitz deformation retraction with estimates on its derivatives. Then, we extend the local inequality to a global inequality by employing double complex technique. As a consequence we obtain an isomorphism between Lᵖ cohomology and singular cohomology of a normal compact semialgebraic pseudomanifold.