The Hardy inequality and the heat flow in curved wedges

David Krejcirik

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arXiv · 1507.03627

The Hardy inequality and the heat flow in curved wedges

David Krejcirik

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Abstract

We show that the polynomial decay rate of the heat semigroup of the Dirichlet Laplacian in curved planar wedges equals the sum of the usual dimensional decay rate and a multiple of the reciprocal value of the opening angle. To prove the result, we develop the method of self-similar variables for the associated heat equation and study the asymptotic behaviour of the transformed non-autonomous parabolic problem for large times. We also establish an improved Hardy inequality for the Dirichlet Laplacian in non-trivially curved wedges and state a conjecture about an improved decay rate in this case.

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BibTeX RIS

David Krejcirik. 2015-07-13. The Hardy inequality and the heat flow in curved wedges. https://arxiv.org/abs/1507.03627

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