Abstract

The existence, regularity and uniqueness of a local diffeomorphism phi satisfying g(i)(phi) det del phi = f(i) for 1 <= i <= n is discussed.

Highlights

  • Given functions gi and fi we wish to discuss the existence of a local di¤eomorphism ' solving gi (') det r' = fi for every 1 i n: (1)

  • The case of one equation was ...rst considered in the seminal paper of Moser [4]

  • We obtain uniqueness of solutions, in sharp contrast with the classical case of one equation, once the solution is prescribed on a non-characteristic (n 1) surface

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Summary

Introduction

Where 2 Cr 1: Using the method of characteristics, we can ...nd, near 0; u 2 Cr 1 verifying the last equation as well as u (0) = 0: This concludes the proof of the existence part.

Results
Conclusion
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