Moser-trudinger inequalities without boundary conditions and isoperimetric problems

@inproceedings{Cianchi2005MosertrudingerIW,
  title={Moser-trudinger inequalities without boundary conditions and isoperimetric problems},
  author={Andrea Cianchi},
  year={2005}
}
The best constant is exhibited in Trudinger's exponential inequality for functions from the Sobolev space W 1,n (Ω), with Ω c R n and n ≥ 2. This complements a classical result by Moser dealing with the subspace W 1,n 0 (Ω). An extension to the borderline Lorentz-Sobolev spaces W 1 L n,1 (Ω) with 1 < q < ∞ is also established. A key step in our proofs is an asymptotically sharp relative isoperimetric inequality for domains in R n .