# The Hardy inequality and the heat flow in curved wedges

@article{Krejik2015TheHI, title={The Hardy inequality and the heat flow in curved wedges}, author={D. Krej{\vc}iř{\'i}k}, journal={arXiv: Spectral Theory}, year={2015} }

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… CONTINUE READING

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