IJPAM: Volume 77, No. 3 (2012)
A VARIATIONAL PRINCIPLE AND ITS APPLICATION
A.G. Ramm
Department of Mathematics
Kansas State University
Manhattan, KS 66506, USA
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





where






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
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 3