A BOUNDARY INTEGRAL EQUATIONS APPROACH FOR MIXED IMPEDANCE PROBLEMS IN ELASTICITY

作者：Athanasiadis C E; Natroshvili D^*; Sevroglou V; Stratis I G

来源：Journal of Integral Equations and Applications, 2011, 23(2): 183-222.

DOI：10.1216/JIE-2011-23-2-183

• Elasticity
• elastic oscillations
• mixed boundary value problems
• impedance problems
• potential method
• pseudodifferential equations
• elastic radiation conditions

Direct scattering problems for partially coated obstacles in linear elasticity lead to interior and exterior mixed impedance boundary value problems for the equations of steady-state elastic oscillations. We employ the potential method and reduce the mixed impedance problems to equivalent boundary pseudodifferential equations for arbitrary values of the oscillation parameter. We give a detailed analysis of the corresponding pseudodifferential equations which live on a proper submanifold of the boundary of the elastic body and establish uniqueness and existence results for the original mixed impedance problems for arbitrary values of the oscillation parameter; this is crucial in the study of inverse elastic scattering problems for partially coated obstacles. We also investigate regularity properties of solutions near the curves where the boundary conditions change and establish almost best Holder smoothness results.

• 出版日期2011