TY - THES
TI - Estudio básico de la existencia y unicidad de la solución para el problema de Dirichlet a través del método de Perrón
AU - Nova Martínez, Manuel Arturo
AB - In this work we study the existence and uniquessly of solution for the Dirichlet problem, where
is an open, connected and bounded subset de RN, f is a continuous scalar eld on and g is continuous on the boundary of. For the case f = 0 some properties of the harmonic fuctions are analyzed and the existence of the solution is demostrated by the Perron method, this under a certain hypothesis of regularity of the domain boundary. In the general case the fundamental solution of the Laplace equation is constructed based on the properties of operator Laplaciano symmetry, a formula of integral representation for the solution fuction is deduced and it is demostrated that the solution veri es the problem data. Finally some geometric criteria that ensure the regularity in the boundary points are presented.
DA - 2018
PB - Universidad Pedagógica y Tecnológica de Colombia
UR - https://repositorio.uptc.edu.co/handle/001/2650
ER -