Harmonic Function of Poincare Cone Condition In Solving Dirichlet Problem

Abstract

This paper describes the set of harmonic functions on a given open set U which can be seen as the kernel of the Laplace operator and is therefore a vector space over R .It also reviews the harmonic theorem, the dirichlet problem and maximum principle where we conclude that the application of sums , differences and scalar multiples of harmonic functions are again harmonic.

Keywords: Harmonic, maximum principles, Vector space, Poincare cone, Holder condition.

Journal of the Nigerian Association of Mathematical Physics, Volume 20 (March, 2012), pp 17 – 22