Alguns resultados sobre o operador de Laplace

Abstract

The purpose of this work is to study facts and applications about the Laplacian, a di erential operator that plays a crucial role in many physical phenomena. We will show the behavior of the Laplace operator under the action of rotations and translations and it will brie y be discussed the eingenvalue problem for some speci c Euclidean domains, as well as some basic properties of harmonic functions. A geometrical signi cance of the Laplacian will also be presented.