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Solution of boundary and eigenvalue problems for second-order elliptic operators in the plane using pseudoanalytic formal powers. (English) Zbl 1210.35054
Summary: 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.
MSC:
35J25Second order elliptic equations, boundary value problems
35P05General topics in linear spectral theory of PDE
35J10Schrödinger operator
31A25Boundary value and inverse problems (two-dimensional potential theory)
30G20Generalizations of analytic functions of Bers or Vekua type
30E25Boundary value problems, complex analysis