Abstract
This article is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green's formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different parts of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spaces.
Acknowledgments
The research of Fioralba Cakoni was supported in part by the Air Force Office of Scientific Research under Grant F49620-02-1-0353. The research of George C. Hsiao and Wolfgang L. Wendland was supported in part by the German Research Foundation DFG under Grant SFB 404 Multifield Problems in Continuum Mechanics.
Notes
Dedicated to Heinrich Begehr on the occasion of his 65th birthday.