On Riemann Boundary Value Problems for Certain Linear Elliptic Systems in the Plane.
DELAWARE UNIV NEWARK INST FOR MATHEMATICAL SCIENCES
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The partial differential equations which occur in the theory of elastic plates and shells are among those which may be reduced to a first order elliptic system. Under certain regularity conditions for the coefficients, a Beltrami transformation exists taking the general first-order, elliptic systems into a normal-Douglis-form. This form can be further simplified, and more concisely represented by utilizing the algebra of hypercomplex numbers. The theory of solutions to these linear systems is known as generalized hyperanalytic function theory. The present work deals with Riemann boundary value problems for linear systems. It is shown that every solution of the homogeneous boundary value problem may be written as a linear combination of special solutions resembling Bers generating pairs. The nonhomogeneous solution is represented as a homogeneous solution plus a particular solution which is given as an integral representation using a generalized Cauchy kernel.
- Numerical Mathematics