Abstract:
We consider boundary-value problems in the upper half-plane for second-order
elliptic systems with constant higher coefficients. Using the Bitsadze
transformation, we reduce these problems to equivalent problems for analytic
functions. This approach enables us to obtain explicit formulae for the
solutions of basic boundary-value problems and to study the Fredholm solubility
of these problems. (In particular, we obtain an analytic expression for the
index.) We work in weighted Hölder and Hardy spaces.
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