The mapping properties of the radiosity operator along an edge

✍ Scribed by Olaf Hansen

• Book ID: 102510970
• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 145 KB
• Volume: 25
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.329

✦ Synopsis

Abstract

In this article we study the radiosity operator along an edge between two adjacent half‐planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half‐planes, the reflectivity coefficients and the right‐hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22: 217–241). Copyright © 2002 John Wiley & Sons, Ltd.