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The Hardy inequality and the heat flow in curved wedges
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SYSNO ASEP 0460657 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Hardy inequality and the heat flow in curved wedges Author(s) Krejčiřík, David (UJF-V) RID Number of authors 1 Source Title Portugaliae Mathematica - ISSN 0032-5155
Roč. 73, č. 2 (2016), s. 91-113Number of pages 23 s. Publication form Print - P Language eng - English Country PT - Portugal Keywords Hardy inequality ; heat equation ; large-time behaviour ; curved wedges ; Dirichlet Laplacian ; conical singularities ; Brownian motion ; subcriticality Subject RIV BE - Theoretical Physics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000377323000001 EID SCOPUS 84962840840 DOI 10.4171/PM/1978 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2017
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