Boundary regularity for the supercritical Lane-Emden heat flow
type: Item
instance of: scholarly article
title: Boundary regularity for the supercritical Lane-Emden heat flow
zbMATH Open document ID: 1327.35193
author: Simon Blatt
author: Michael Struwe
published in: Calculus of Variations and Partial Differential Equations
publication date: 2015-10-14T00:00:00Z
full work available at URL: 526 2015 Article 865.pdf
review text: The authors considers the Lane-Emden heat flow \(u_t-\Delta u=|u|^{p-2}u\) on a smooth bounded domain \(\Omega\subset \mathbb{R}^n\) with \(n\geq3\), in the supercritical case \(p>2^{*}=\frac{2n}{n-2}\). Extending their previous results on the problem, they establish a Pacard-type monotonicity formula and Morrey bounds up to the boundary. As an important consequence, they obtain partially regular, self-similar tangent maps at any first blow-up point of the flow, and partial regularity at the blow-up time if the energy is uniformly bounded from below.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35K91
zbMATH DE Number: 6494070
zbMATH Keywords: Lane-Emden heat flow
zbMATH Keywords: Morrey spaces
zbMATH Keywords: Pacard-type monotonicity
MaRDI profile type: Publication
OpenAlex ID: W616145310
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DOI: 10.1007/S00526-015-0865-7
description: scientific article; zbMATH DE number 6494070