%0 Journal Article
%T A short proof of the existence of the solution to elliptic boundary problem
%A Alexander G. Ramm
%J -
%D 2015
%R 10.14419/gjma.v3i3.4731
%X There are several methods for proving the existence of the solution to the elliptic boundary problem \(Lu=f \text{in} D,\quad u|_S=0,\quad (*)\). Here L is an elliptic operator of second order, f is a given function, and uniqueness of the solution to problem (*) is assumed. The known methods for proving the existence of the solution to (*) include variational methods, integral equation methods, method of upper and lower solutions. In this paper a method based on functional analysis is proposed. This method is conceptually simple. It requires some a priori estimates and a continuation in a parameter method, which is well-known.
%U https://www.sciencepubco.com/index.php/GJMA/article/view/4731