A note on immersions of domains of fractional powers of certain sectorial operators in Sobolev spaces
type: Item
instance of: scholarly article
title: A note on immersions of domains of fractional powers of certain sectorial operators in Sobolev spaces
zbMATH Open document ID: 1255.46018
author: Anderson De Araújo
author: J. L. Boldrini
published in: Applied Mathematics Letters
publication date: 2012-10-11T00:00:00Z
review text: The authors consider the \(L^p\)-realization \(A_p\) of a uniformly strongly elliptic linear operator of order \(2m\) in a bounded domain \(\Omega\) with \(C^{2m}\)-boundary with boundary conditions given by \(m\) linear boundary operators. For fractional powers they show the embedding \(D(A^{\alpha}_p) \hookrightarrow W_p^{2m(1-\frac{1}{p})}(\Omega)\) for all \(p > 2m\) and \(0 < \alpha < 1\) with \(\frac{p-1}{p} < \alpha < 1\), where \(D(A^{\alpha}_p)\) has the graph norm. The proof uses the analyticity of the semigroup generated by \(-A_p\) together with the \(L^p\)-elliptic regularity of the abstract Cauchy problem and trace results. The article concludes with an application of the derived embedding: the existence of an optimal control for a model for mosquito populations is shown.
reviewed by: Stephan Fackler
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 6092778
zbMATH Keywords: embedding theorems for Sobolev spaces
zbMATH Keywords: domains of powers of sectorial operators
zbMATH Keywords: optimal control
zbMATH Keywords: mosquito populations
MaRDI profile type: Publication
full work available at URL: j.aml.2012.05.008
OpenAlex ID: W2088722415
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DOI: 10.1016/J.AML.2012.05.008
description: scientific article; zbMATH DE number 6092778