A limiting case for the divergence equation
نویسندگان
چکیده
We consider the equation div Y = f , with f a zero average function on the torus Td . In their seminal paper [5], Bourgain and Brezis proved the existence of a solution Y ∈W1,d∩L∞ for a datum f ∈ Ld . We extend their result to the critical Sobolev spaces W s,p with (s+1)p = d and p ≥ 2. More generally, we prove a similar result in the scale of Triebel-Lizorkin spaces. We also consider the equation div Y= f in a bounded domain Ω subject to zero Dirichlet boundary condition.
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