On Representation Formulas and Radiation Conditions

✍ Scribed by Martin Costabel; Monique Dauge

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 336 KB
• Volume: 20
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19970125)20:2<133::aid-mma841>3.0.co;2-y

✦ Synopsis

Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework.

Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of 1L or if it is a Green function for an exterior boundary value problem.