Abstract:
We investigate Riesz energy problems on
unbounded conductors in Rd in the presence of general external fields Q.
We provide new sufficient conditions on Q for the existence of an equilibrium measure and
the compactness of its support. Particular attention is paid to the case of the hyperplanar conductor Rd, embedded in Rd+1, when the external field is created by the potential of a simple discrete measure ν outside of Rd.
An extension of a classical theorem by de La Vallée-Poussin is established which may be of independent interest.
This is a joint work with P. Dragnev, R. Orive, and E. B. Saff.