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Benoît Kloeckner
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There might be none. If the boundary of $\Omega$ presents a cusp, then it cannot be flattened even into a corner by a Lipschitz map (in particular, you $\Phi$ must have unbounded first derivative).

Benoît Kloeckner
  • 14.4k
  • 1
  • 60
  • 106