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}
}
  • D. Krejčiřík
  • Published 2015
  • Mathematics, Physics
  • arXiv: Spectral Theory
  • 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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    The asymptotic behaviour of the heat equation in a sheared unbounded strip

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