IJPAM: Volume 67, No. 1 (2011)

THE HODGE-DE RHAM DECOMPOSITION THEOREM
AND AN APPLICATION TO A PARTIAL
DIFFERENTIAL EQUATION

Paul Bracken
Department of Mathematics
University of Texas
Edinburg, TX, 78541-2999, USA
e-mail: [email protected]


Abstract.The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a novel way.

Received: October 27, 2010

AMS Subject Classification: 58A05, 58A10, 47J05

Key Words and Phrases: differential forms, harmonic, decomposition, adjoint

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 1