JournalspmVol. 73, No. 2pp. 91–113

The Hardy inequality and the heat flow in curved wedges

  • David Krejčiřík

    Czech Technical University in Prague, Czech Republic
The Hardy inequality and the heat flow in curved wedges cover
Download PDF

A subscription is required to access this article.

Abstract

We show that the polynomial decay rate of the heat semigroup of the Dirichlet Laplacian in curved planar wedges that are obtained as a compactly supported perturbation of straight 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.

Cite this article

David Krejčiřík, The Hardy inequality and the heat flow in curved wedges. Port. Math. 73 (2016), no. 2, pp. 91–113

DOI 10.4171/PM/1978