theorem A.83 Local canonical form for an elliptic operator with Hölder coefficients

Rests on

• depends_on definition 10.6 Type of a second-order operator ¶
  • depends_on definition 10.4 The second-order operator ¶
    • depends_on definition 10.3 Principal part and principal symbol ¶
      • depends_on definition 10.2 Linear, semilinear, quasilinear ¶
        • depends_on definition 10.1 Partial differential equation; order ¶
      • depends_on equation 10.2 eq:pde-multi-index ¶
    • depends_on proposition 7.105 Clairaut–Schwarz ¶
      • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on equation 7.7 eq:ana-limit-left ¶
        • depends_on equation 7.5 eq:ana-limit-right ¶
      • depends_on theorem 7.35 Mean value theorem ¶
        • depends_on proposition 7.29 Linearity ¶
        • depends_on theorem 7.34 Rolle ¶
        • proves proof ch:05-real-analysis@proof-19 ¶
      • proves proof ch:05-real-analysis@proof-64 ¶
  • depends_on theorem 5.116 Sylvester's law of inertia ¶
    • depends_on definition 5.110 Bilinear map ¶
      • depends_on definition 5.37 Linear transformation ¶
        • depends_on definition 4.33 Vector space ¶
    • depends_on definition 5.111 Symmetric and antisymmetric forms ¶
      • depends_on definition 5.110 Bilinear map ¶ ↺
      • depends_on equation 5.137 eq:lin-bilinear-matrix ¶
    • depends_on equation 5.139 eq:lin-bilinear-congruence ¶
    • proves proof ch:03-linear-algebra-representations@proof-53 ¶
• depends_on equation 10.6 eq:pde-congruence ¶
• depends_on proposition 10.13 Canonical form in two variables ¶
  • depends_on definition 10.10 Characteristic surface ¶
    • depends_on definition 10.4 The second-order operator ¶ ↺
    • depends_on definition 10.3 Principal part and principal symbol ¶ ↺
  • depends_on theorem 10.8 The type is a coordinate invariant ¶
    • depends_on definition 10.6 Type of a second-order operator ¶ ↺
    • depends_on proposition 7.31 Chain rule ¶
      • depends_on definition 7.13 Composite function ¶
        • depends_on definition 7.9 Real function ¶
      • depends_on proposition 7.27 Differentiable implies continuous ¶
        • depends_on definition 7.20 Continuity at a point ¶ ↺
        • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on proposition 7.6 Algebra of limits ¶
        • proves proof ch:05-real-analysis@proof-11 ¶
      • depends_on proposition 7.6 Algebra of limits ¶ ↺
      • proves proof ch:05-real-analysis@proof-15 ¶
    • depends_on theorem 5.116 Sylvester's law of inertia ¶ ↺
    • proves proof ch:08-pdes@proof-1 ¶
  • proves proof ch:08-pdes@proof-4 ¶
  • proves proof ch:08-pdes@prooflink-1 ¶
• proves proof app:A-long-proofs@proof-66 ¶

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