**数学与系统科学研究院**

**计算数学所学术报告**

**报告人**：
W.L. Wendland

Univ. of Stuttgart, Germany

**报告题目**
On Y.Radon's Convergence Proof for C.Neumann's Method with Double Layer Potentials

**Abstract:**
C.Neumann's investigated the boundary integral equation of the second kind with the double layer potential of the Laplacian in 1870 and 1877 and showed for convex regions that a corresponding successive approximation converges uniformly in the space of continuous functions. For smooth-- also nonconvex boundaries (Y. Plemelj) found a relation between the spectrum and the energies of interior and exterior potentials which implies that the spectral radius is less than one. In Y.Radon extended there results in 1919 to boundary curves of bounded rotation for two-dimensional problems, and his foundation of measure theory allowed to extend his approach to nonsmooth boundaries in R3. With appropriate weighted supremum norms we are now able to show stability and convergence of boundary element collocation for a rather large class of Lipschilz domains characterized by a criterion due to O. Hansen.

For Galerlein boundary element methods on Lipschilz boundaries, the Neumann series turns out to converge in energy trace spaces nationally for the double layer operator of the Laplacian but for all positively elliptic systems of second order partial differential equations including the 3-D elasticity system.

**报告时间**：2004年9月10日 上午9：30

**报告地点**：科技综合楼三层报告厅