With this inequality one can immediately prove the uniqueness of solutions of second order hyperbolic equations which are linear, i.e. for which A, B, C and F do not depend on K. For suppose Kuj and K^j were solutions of the equation L(K) = F which had the same initial values and first derivatives on ^f(O) fl <H. Then one can apply the above result to the equation L(K1 — K2) = 0 and obtain

Therefore K1 = K2 on One has thus

Proposition 7.4.5

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