Paris VI and Rutgers
New types of Sobolev-Nirenberg imbeddings, isoperimetric
inequalities and elliptic estimates in
We present new estimates obtained jointly with J. Bourgain, and
partially with P. Mironescu. Each one has a different flavour, but,
in fact, they are closely related.
The first one asserts that
is a closed rectifiable curve,
denotes the length of , is a universal constant
is the tangent to .
The second estimate concerns the classical system, in ,
Our new estimate asserts that
A third new estimate concerns the system
where is a divergence-free vector-field. Our new estimate
Such inequality is unusual because it is well-known that standard
elliptic estimates fail in .