theorem 10.22 Cauchy–Kovalevskaya

Rests on

• depends_on definition 10.2 Linear, semilinear, quasilinear ¶
  • 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 7.16 Limit ¶
        • depends_on equation 7.7 eq:ana-limit-left ¶
        • depends_on equation 7.5 eq:ana-limit-right ¶
      • depends_on definition 7.97 Partial derivative; gradient ¶
        • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on definition 5.15 Basis ¶
    • depends_on definition 6.2 Open set ¶
      • depends_on definition 6.1 Topological space ¶
        • depends_on definition 3.31 Empty set ¶
        • depends_on definition 3.35 Union, intersection, difference ¶
        • depends_on definition 3.30 Subset ¶
        • depends_on equation 3.51 eq:set-indexed ¶
• depends_on proposition 10.11 What a characteristic surface is ¶
  • 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 definition 10.2 Linear, semilinear, quasilinear ¶ ↺
        • 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 theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-64 ¶
    • 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 definition 10.4 The second-order operator ¶ ↺
      • depends_on theorem 5.116 Sylvester's law of inertia ¶
        • depends_on definition 5.110 Bilinear map ¶
        • depends_on definition 5.111 Symmetric and antisymmetric forms ¶
        • depends_on equation 5.139 eq:lin-bilinear-congruence ¶
        • proves proof ch:03-linear-algebra-representations@proof-53 ¶
    • 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-2 ¶
• proves proof app:A-long-proofs@proof-73 ¶
• proves proof ch:08-pdes@prooflink-2 ¶

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