Accession Number:
ADA141748
Title:
On the Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 6. Manifolds in Euclidean Spaces, Regularity Properties of Domains.
Descriptive Note:
Final technical rept.,
Corporate Author:
DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST
Personal Author(s):
Report Date:
1984-04-01
Pagination or Media Count:
190.0
Abstract:
Various standard results concerning manifolds in euclidean spaces, coordinate systems, and functions defined on such manifolds are developed and organized. For example, conditions are identified under which the image of a manifold is again a manifold. A development of Lebesgue measure and integration on a manifold is presented. Included is a change-of-variables formula for the transformation of an integral over a manifold to integration over a second manifold suitably related to the first. Classes of regular domains are defined. Special attention is given to those regular domains possessing a Holder-continuous exterior unit normal field, or Lyapunov domains. Slightly modifying the standard presentations, geometric and analytic properties of the boundary of a Lyapunov domain are derived, including the identification of certain canonical tangent-plane coordinate systems. Author
Descriptors:
Subject Categories:
- Theoretical Mathematics
- Electricity and Magnetism
- Optics