On elliptic boundary value problems on upper half-plane

Abstract

The boundary value problems for elliptic systems of the second order with leading and constant coefficients are considered in a half-plane. The investigation is based on the Bitsadze formula which represents a general solution of this system through a vector-valued analytic function. The transformation of this formula is studied in Holder spaces with weight. As a consequence, the explicit formulas of the solution to the problems are received. The applications to anisotropic elasticity are also given.

Keywords:

• Elliptic systems
• Constant coefficients
• Half-plane
• Analytic functions
• Boundary value problems
• Explicit representations
• AMS Subject Classifications: 30E25
• 35J55

Acknowledgements

The work was supported in part by the Russian Foundation of Basic Reasearch RFBR (project No. 02-01-00623) and by the program of Russian Universities (project No. UR 04.01.486).

Notes

Dedicated to Professor Dr. Heinrich G.W. Begehr on his 65th birthday.

Additional information

Notes on contributors

A. Soldatov

Dedicated to Professor Dr. Heinrich G.W. Begehr on his 65th birthday.