Spectral analysis for a discontinuous second order elliptic operator

The spectrum of a second order elliptic operator S, with ellipticity constant α discontinuous in a point, is studied in L^p spaces. It turns out that, for (α, p) in a set A, classical re...

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Main Authors:	Paolo Manselli, Francesco Ragnedda
Format:	Article
Language:	English
Published:	Università degli Studi di Catania 2003-05-01
Series:	Le Matematiche
Online Access:	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/181

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spelling	doaj-c4ebfb4abb5e41ada6ea9f3cef1ec5b12020-11-25T03:34:15ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982003-05-015816793159Spectral analysis for a discontinuous second order elliptic operatorPaolo ManselliFrancesco Ragnedda<p>The spectrum of a second order elliptic operator <em>S</em>, with ellipticity constant <em>α</em> discontinuous in a point, is studied in <em>L^p</em> spaces. It turns out that, for <em>(α, p)</em> in a set <em>A</em>, classical results for the spectrum of smooth elliptic operators (see e.g. [3]) remain true for <em>S</em>; in particular, it is proved that <em>S</em> is the infinitesimal generator of an holomorphic semigroup . If <em>(α, p)</em> not in<em> A</em>, then the spectrum of <em>S</em> is the whole complex plane.</p>http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/181
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Paolo Manselli Francesco Ragnedda
spellingShingle	Paolo Manselli Francesco Ragnedda Spectral analysis for a discontinuous second order elliptic operator Le Matematiche
author_facet	Paolo Manselli Francesco Ragnedda
author_sort	Paolo Manselli
title	Spectral analysis for a discontinuous second order elliptic operator
title_short	Spectral analysis for a discontinuous second order elliptic operator
title_full	Spectral analysis for a discontinuous second order elliptic operator
title_fullStr	Spectral analysis for a discontinuous second order elliptic operator
title_full_unstemmed	Spectral analysis for a discontinuous second order elliptic operator
title_sort	spectral analysis for a discontinuous second order elliptic operator
publisher	Università degli Studi di Catania
series	Le Matematiche
issn	0373-3505 2037-5298
publishDate	2003-05-01
description	<p>The spectrum of a second order elliptic operator <em>S</em>, with ellipticity constant <em>α</em> discontinuous in a point, is studied in <em>L^p</em> spaces. It turns out that, for <em>(α, p)</em> in a set <em>A</em>, classical results for the spectrum of smooth elliptic operators (see e.g. [3]) remain true for <em>S</em>; in particular, it is proved that <em>S</em> is the infinitesimal generator of an holomorphic semigroup . If <em>(α, p)</em> not in<em> A</em>, then the spectrum of <em>S</em> is the whole complex plane.</p>
url	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/181
work_keys_str_mv	AT paolomanselli spectralanalysisforadiscontinuoussecondorderellipticoperator AT francescoragnedda spectralanalysisforadiscontinuoussecondorderellipticoperator
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Spectral analysis for a discontinuous second order elliptic operator

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