4. Variational formulation of elliptic boundary problems
In this section, we show how the introduced Sobolev spaces are used to solve elliptic boundary partial differential equations. We will simply illustrate this with the two classical problems, the Dirichlet problem and the Neumann problem for a regular bounded open Ω of .
4.1 Dirichlet problem
The Dirichlet problem in an open disk D of is the following: find a function u of class
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Variational formulation of elliptic boundary problems
Application to second-order stationary processes
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