IJPAM: Volume 77, No. 3 (2012)
Department of Mathematics
Kansas State University
Manhattan, KS 66506, USA
Abstract. Assume that is a bounded selfadjoint operator in a Hilbert space . Then, the variational principle
holds if and only if , that is, if for all . We define the left-hand side in (*) to be zero if . As an application of this principle it is proved that
where is the -space of real-valued functions on the connected surface of a bounded domain , and is the electrical capacitance of a perfect conductor .
The classical Gauss' principle for electrical capacitance
is an immediate consequence of (*).
Received: April 12, 2012
AMS Subject Classification: 35J05, 47A50
Key Words and Phrases: variational principle, capacitance
Download paper from here.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395