proposition 30.50 Love waves need a slow surface layer

Rests on

• depends_on definition 30.22 Boundary conditions of elastostatics ¶
  • depends_on definition 10.24 Well-posed problem ¶
    • depends_on definition 10.1 Partial differential equation; order ¶
      • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.97 Partial derivative; gradient ¶
      • depends_on definition 6.2 Open set ¶
        • depends_on definition 6.1 Topological space ¶
    • depends_on definition 6.24 Metric ¶
      • depends_on definition 3.43 Map ¶
        • depends_on definition 3.24 Quantifiers ¶
        • depends_on definition 3.28 Set ¶
      • depends_on definition 3.38 Ordered pair and Cartesian product ¶
  • depends_on theorem 30.21 Cauchy's equation of motion ¶
    • depends_on theorem 7.133 Gauss ¶
      • depends_on definition 7.127 Simple regions ¶
        • depends_on definition 7.98 Functions of class $C^{1}$ ¶ ↺
        • depends_on definition 6.9 Compact set ¶
      • depends_on remark 7.128 What the derivations below take as given ¶
        • depends_on definition 7.125 Multiple integral ¶
        • depends_on theorem 7.40 Continuous functions are integrable ¶
        • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • depends_on definition 7.41 Antiderivative ¶
        • depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
        • proves proof ch:05-real-analysis@proof-25 ¶
      • proves proof ch:05-real-analysis@proof-79 ¶
    • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      • depends_on definition 30.17 Traction ¶
        • depends_on definition 7.126 Line and surface integrals ¶
        • depends_on definition 30.2 Representative volume element; continuum field ¶
      • depends_on definition 13.5 Tensor under orthogonal transformations ¶
        • depends_on definition 13.4 Orthogonal coordinate transformation ¶
      • proves proof ch:13-continuum-elasticity@proof-7 ¶
    • proves proof ch:13-continuum-elasticity@proof-9 ¶
• depends_on theorem 30.40 Navier–Cauchy equations ¶
  • depends_on equation 30.21 eq:elast-hooke-isotropic ¶
  • depends_on theorem 30.21 Cauchy's equation of motion ¶ ↺
  • proves proof ch:13-continuum-elasticity@proof-18 ¶
• proves proof ch:13-continuum-elasticity@proof-26 ¶

Supports

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