However, for the methods using Dirichlet conditions
, the choice is more difficult since the gap in the spectrum is smaller.
. We consider the following equation with Dirichlet boundary conditions:
Boundary conditions may be in the form of Dirichlet conditions
Here we introduce the solution of 2D Laplace equation with Dirichlet conditions
in order to declare the basic idea of the method.
In this paper, we study the following gradient nonlinear elliptic system with Dirichlet conditions
He proposed that the homogeneous Dirichlet conditions
may be satisfied exactly by representing the solution as the product of two functions: (1) an real-valued function that takes on zero values on the boundary points; and (2) an unknown function that allows to satisfy (exactly or approximately) the differential equation of the problem.
In the article titled "On a Nonlinear Wave Equation Associated with Dirichlet Conditions
: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters" , there are similarities with two of the authors' previous publications; one of them was cited:
Considering the Dirichlet conditions
at x = 0 and x = [x.sub.5] and the magnetic vector potential finite at y = +[infinity], the general solution of (1) can be expressed as
This field satisfies the Dirichlet conditions
at all four sides.
where [GAMMA] symbolizes the boundary, and the Dirichlet conditions
are considered at 20[degrees]C for natural convective air-cooling BEM formulation, Green's function as a solution of the Equation (2) through (7) as follows.
The inhomogeneous polyanalytic equation is studied by Begehr and Kumar  in D with Dirichlet conditions
and the following result is obtained.
are assumed on a closed subset [[GAMMA].sub.D] of [GAMMA], while Neumann boundary conditions are assumed on [[GAMMA].sub.N] := [GAMMA]/[[GAMMA].sub.D].