Spectral analysis for a discontinuous second order elliptic operator
<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 re...
| Main Authors: | , |
|---|---|
| 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 |
| Summary: | <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> |
|---|---|
| ISSN: | 0373-3505 2037-5298 |