A short proof of the existence of the solution to elliptic boundary problem
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2015-06-06 https://doi.org/10.14419/gjma.v3i3.4731 -
Dynamical systems method (DSM), Homeomorphism, Nonlinear equations, Surjectivity -
Abstract
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.
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References
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How to Cite
Ramm, A. G. (2015). A short proof of the existence of the solution to elliptic boundary problem. Global Journal of Mathematical Analysis, 3(3), 105-108. https://doi.org/10.14419/gjma.v3i3.4731Received date: 2015-05-07
Accepted date: 2015-06-02
Published date: 2015-06-06