Carleman inequalities and the heat operator
type: Item
instance of: scholarly article
title: Carleman inequalities and the heat operator
zbMATH Open document ID: 0979.35029
DOI: 10.1215/S0012-7094-00-10415-2
author: L. Escauriaza
published in: Duke Mathematical Journal
publication date: 2002-02-21T00:00:00Z
review text: The paper refers to the strong unique continuation property for parabolic equations with time-dependent coefficients. The strong unique continuity result for the heat operator is derived from a Carleman inequality: \[ \|t^{-\varepsilon} e^{-|x|^{2/8t}}f\|_{L^q_tL^p_x}\leq N(n,r,s,\mu)\|t^{-\alpha+1-(n/2r)-(1/s)}e^{-|x|^2/8t}(\Delta f+\partial_tf)\|_{L^p_t L^p_x} \] which holds under special assumptions for the parameters and for any \(f\in C^\infty_0(\mathbb{R}^{n+1}\setminus\{(0,0)\})\). This estimation is proved first and is actually the central result of the paper.
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1501667
zbMATH Keywords: strong unique continuation
zbMATH Keywords: parabolic equations with time-dependent coefficients
MaRDI profile type: Publication
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full work available at URL: s0012-7094-00-10415-2
OpenAlex ID: W1978741530
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description: scientific article; zbMATH DE number 1501667