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Table of Contents XIX

9.3.2 The Hypersingular Operator for the Lam´e System . . . . 531
9.3.3 The Hypersingular Operator for the Stokes System . . . 535
9.4 Derivatives of Boundary Potentials . . . . . . . . . . . . . . . . . . . . . . . 535
9.4.1 Derivatives of the Solution to the Helmholtz Equation 541
9.4.2 Computation of Stress and Strain on the Boundary
for the Lam´e System .............................. 543
9.5 Remarks .............................................. 547
2
10. Boundary Integral Equations on Curves in IR ............ 549
10.1 Fourier Series Representation of the Basic Operators . . . . . . . . 550
10.2 The Fourier Series Representation of Periodic Operators
m
A ∈L (Γ) ............................................ 556
c
10.3 Ellipticity Conditions for Periodic Operators on Γ .......... 562
10.3.1 Scalar Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
10.3.2 Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568
10.3.3 Multiply Connected Domains . . . . . . . . . . . . . . . . . . . . . . 572
10.4 Fourier Series Representation of some Particular Operators . . 574
10.4.1 The Helmholtz Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 574
10.4.2 The Lam´e System ................................ 578
10.4.3 The Stokes System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581
10.4.4 The Biharmonic Equation . . . . . . . . . . . . . . . . . . . . . . . . . 582
10.5 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

A. Differential Operators in Local Coordinates
with Minimal Differentiability ............................ 593

References .................................................... 599

Index ......................................................... 613