The Dirichlet problem for elliptic systems in multiconnected rough regions

Abstract

We present a new integral formulation for the L ² Dirichlet boundary value problem associated with second order elliptic systems in multiconnected regions with rough boundaries. This study has been motivated by displacement prescribed problems arising in solid mechanics and our results are relevant to their numerical treatment.

Keywords:

• Elliptic systems
• Dirichlet problem
• Multiconnected domains
• Layer potentials
• Lamé system
• 2000 Mathematics Subject Classifications: Primary: 45E05
• 47A05
• Secondary: 35J25
• 42B20

Acknowledgements

This study was supported in part by NSF Grant DMS 0513173 and a FEST Grant from the University of Virginia. The first and last authors were supported by NSF Grant CMS-9912524 to Cornell University.