Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers. (arXiv:1002.1110v1 [math.AP])

Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers. (arXiv:1002.1110v1 [math.AP]): "

We propose a method for solving boundary value and eigenvalue problems for
the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function
theory and in particular pseudoanalytic formal powers. Under certain conditions
on the coefficients p and q with the aid of pseudoanalytic function theory a
complete system of null solutions of the operator can be constructed following
a simple algorithm consisting in recursive integration. This system of
solutions is used for solving boundary value and spectral problems for the
operator D in bounded simply connected domains. We study theoretical and
numerical aspects of the method.

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