Some properties of the operators of potential theory and their application to the investigation of the basic equation of electrostatics and magnetostatics
Some new properties are proved for the operator B* of the direct value of the potential of a double layer on a closed surface S = {partial_derivative}{Omega}, in particular the existence in H{sup 1/2}(S) of a basis of eigenfunctions. On the basis of these properties it is proved that the vector integral equation {alpha}M(x) + {del}{integral}{sub {Omega}} M(y){del}{sub y}{vert_bar}x-y{vert_bar}dy = H(x), {alpha} {ge} 0, {Omega} {contained_in} R{sup 3}, which is encountered in classical problems of electro- and magnetostatics, is equivalent to the well-known scalar equation with operator B*. The properties of the operator on the left-hand side and of the solutions of the vector equations are investigated.
- OSTI ID:
- 102937
- Journal Information:
- Theoretical and Mathematical Physics, Journal Name: Theoretical and Mathematical Physics Journal Issue: 3 Vol. 100; ISSN 0040-5779; ISSN TMPHAH
- Country of Publication:
- United States
- Language:
- English
Similar Records
Low energy resolvent bounds for elliptic operators: An application to the study of waves in stratified media and fiber optics
Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential