Heat flow for Dirichlet-to-Neumann operator with critical growth
type: Item
instance of: scholarly article
title: Heat flow for Dirichlet-to-Neumann operator with critical growth
zbMATH Open document ID: 1391.35199
author: Fei Fang
author: Zhong Tan
published in: Advances in Mathematics
publication date: 2018-03-15T00:00:00Z
review text: The authors study the heat flow equation for the Dirichlet-to-Neumann operator with critical growth. More precisely, the authors consider the case that the initial value is lower-energy, i.e. \(E(v_0) <\frac{1}{2N}S^N\) where \(S\) is the best Sobolev constant, \[ E(v_0) = \frac12 \int_{\Omega\times(0,\infty)}|\nabla v_0(t)|^2dxdy - \frac{1}{2^\ast}\int_{\Omega \times\{0\}}|v(t)| ^{2^\ast} dx \] and \(2^\ast\) is \( \frac{2N}{N-1}\). Under such an assumption, the authors study the existence, blowup and regularity of the solutions. Lastly they prove also that a concentration phenomenon of the solution when the time goes to infinity occurs.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6850682
zbMATH Keywords: Dirichlet-to-Neumann operator
zbMATH Keywords: critical growth
zbMATH Keywords: blowup
zbMATH Keywords: global solutions
zbMATH Keywords: concentration phenomenon
MaRDI profile type: Publication
full work available at URL: j.aim.2018.01.010
OpenAlex ID: W2792951612
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DOI: 10.1016/J.AIM.2018.01.010
description: scientific article; zbMATH DE number 6850682