On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$

Leonid Shartser

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arXiv · 1107.0240

On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$

Leonid Shartser

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Abstract

We study Poincar\'e type $L^p$ inequality on a compact semialgebraic subset of $\R^n$ 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 $L^p$ cohomology and singular cohomology of a normal compact semialgebraic pseudomanifold.

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BibTeX RIS

Leonid Shartser. 2011-07-01. On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$. https://arxiv.org/abs/1107.0240

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