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2 Local Existence

In this section basic facts about local existence theorems for the Einstein equations are recalled. Since the theory is well developed and good accounts exist elsewhere (see for instance [148Jump To The Next Citation Point]), attention is focussed on remaining open questions known to the author. In particular, the questions of the minimal regularity required to get a well-posed problem and of free boundaries for fluid bodies are discussed.


 2.1 The constraints
 2.2 The vacuum evolution equations
 2.3 Questions of differentiability
 2.4 New techniques for rough solutions
 2.5 Matter fields
 2.6 Free boundary problems

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